5 Best Ways to Find the Removed Term from an Arithmetic Sequence in Python

by 
def find_missing_set(seq, start, end, step):
    full_set = set(range(start, end + step, step))
    given_set = set(seq)
    missing = full_set - given_set
    return missing.pop() if missing else None

sequence = [3, 7, 15, 19]
missing_number = find_missing_set(sequence, 3, 19, 4)
print(f"The missing number is: {missing_number}")

The output of this code snippet:

The missing number is: 11

This code snippet creates a complete set from the beginning to end of where the sequence should span and then subtracts the set of the given sequence from it. The result is the set of missing numbers, from which the missing term can be extracted.

Method 4: Leveraging Arithmetic Sequence Formula

By using the arithmetic sequence formula \(a_n = a_1 + (n – 1) * d\), where \(a_n\) is the nth term, \(a_1\) is the first term, and \(d\) is the common difference, we can precisely calculate each term. Comparing the calculated terms against the given sequence, we can spot the removed term.

Here’s an example:

def find_missing_formula(seq):
    diff = (seq[-1] - seq[0]) // len(seq)
    for i, value in enumerate(seq):
        if value != seq[0] + i * diff:
            return seq[0] + i * diff
    return None

sequence = [3, 7, 11, 19]
missing_number = find_missing_formula(sequence)
print(f"The missing term is: {missing_number}")

The output of this code snippet:

The missing term is: 15

This snippet relies on the formula for an arithmetic sequence to deduce what each term should be. When it encounters a value in the sequence that doesn’t match the calculated value, it returns the expected value which corresponds to the missing term.

Bonus One-Liner Method 5: List Comprehension with Enumeration

This one-liner leverages list comprehension and the enumerate function in Python to quickly identify the missing term in an arithmetic sequence. It is a concise and Pythonic way of addressing the problem.

Here’s an example:

sequence = [3, 7, 15, 19]
diff = (sequence[-1] - sequence[0]) // len(sequence)
missing_number = next(sequence[0] + i * diff for i, num in enumerate(sequence) if num != sequence[0] + i * diff)
print(f"The missing term is: {missing_number}")

The output of this code snippet:

The missing term is: 11

This one-liner uses a generator expression with the next function to iterate over enumerated sequence items. It immediately returns the first missing term found without having to process the entire sequence.

Summary/Discussion

  • Method 1: Calculate Using Average. This method is straightforward and efficient, suitable for sequences where the first and last terms are known. However, it’s not applicable if the sequence is unordered or these terms are missing.
  • Method 2: Use Sequence Properties. This approach is methodical and does not require knowledge of all sequence terms, making it versatile. However, it is not the most efficient for very long sequences since it requires iterating through all terms until the missing one is found.
  • Method 3: Using Set Differences. It is intuitive and works well when the complete range of the sequence is known, but it can be less efficient with very large sequences due to the cost of creating sets.
  • Method 4: Leveraging Arithmetic Sequence Formula. This method is precise and follows a mathematical approach, which is a reliable way to find the missing term. It may be slightly less efficient than the average method as it relies on an iterative comparison.
  • Method 5: List Comprehension with Enumeration. The one-liner is the most Pythonic, using features of the language to provide a compact solution. It’s best for developers comfortable with list comprehensions and generator expressions.
def find_removed_term(seq):
    diff = (seq[-1] - seq[0]) // len(seq)
    for i in range(len(seq) - 1):
        if seq[i+1] - seq[i] != diff:
            return seq[i] + diff
    return None

sequence = [3, 7, 15, 19]
missing_number = find_removed_term(sequence)
print(f"Removed term: {missing_number}")

The output of this code snippet:

Removed term: 11

This snippet finds the expected common difference and then iterates through the provided sequence looking for the point where the difference between two terms does not match this expected difference. The missing term is then returned.

Method 3: Using Set Differences

The set difference method involves creating a complete set of numbers for the arithmetic sequence and then using set subtraction to find the missing term. This is an intuitive approach but requires knowledge of the common difference and the range of numbers.

Here’s an example:

def find_missing_set(seq, start, end, step):
    full_set = set(range(start, end + step, step))
    given_set = set(seq)
    missing = full_set - given_set
    return missing.pop() if missing else None

sequence = [3, 7, 15, 19]
missing_number = find_missing_set(sequence, 3, 19, 4)
print(f"The missing number is: {missing_number}")

The output of this code snippet:

The missing number is: 11

This code snippet creates a complete set from the beginning to end of where the sequence should span and then subtracts the set of the given sequence from it. The result is the set of missing numbers, from which the missing term can be extracted.

Method 4: Leveraging Arithmetic Sequence Formula

By using the arithmetic sequence formula \(a_n = a_1 + (n – 1) * d\), where \(a_n\) is the nth term, \(a_1\) is the first term, and \(d\) is the common difference, we can precisely calculate each term. Comparing the calculated terms against the given sequence, we can spot the removed term.

Here’s an example:

def find_missing_formula(seq):
    diff = (seq[-1] - seq[0]) // len(seq)
    for i, value in enumerate(seq):
        if value != seq[0] + i * diff:
            return seq[0] + i * diff
    return None

sequence = [3, 7, 11, 19]
missing_number = find_missing_formula(sequence)
print(f"The missing term is: {missing_number}")

The output of this code snippet:

The missing term is: 15

This snippet relies on the formula for an arithmetic sequence to deduce what each term should be. When it encounters a value in the sequence that doesn’t match the calculated value, it returns the expected value which corresponds to the missing term.

Bonus One-Liner Method 5: List Comprehension with Enumeration

This one-liner leverages list comprehension and the enumerate function in Python to quickly identify the missing term in an arithmetic sequence. It is a concise and Pythonic way of addressing the problem.

Here’s an example:

sequence = [3, 7, 15, 19]
diff = (sequence[-1] - sequence[0]) // len(sequence)
missing_number = next(sequence[0] + i * diff for i, num in enumerate(sequence) if num != sequence[0] + i * diff)
print(f"The missing term is: {missing_number}")

The output of this code snippet:

The missing term is: 11

This one-liner uses a generator expression with the next function to iterate over enumerated sequence items. It immediately returns the first missing term found without having to process the entire sequence.

Summary/Discussion

  • Method 1: Calculate Using Average. This method is straightforward and efficient, suitable for sequences where the first and last terms are known. However, it’s not applicable if the sequence is unordered or these terms are missing.
  • Method 2: Use Sequence Properties. This approach is methodical and does not require knowledge of all sequence terms, making it versatile. However, it is not the most efficient for very long sequences since it requires iterating through all terms until the missing one is found.
  • Method 3: Using Set Differences. It is intuitive and works well when the complete range of the sequence is known, but it can be less efficient with very large sequences due to the cost of creating sets.
  • Method 4: Leveraging Arithmetic Sequence Formula. This method is precise and follows a mathematical approach, which is a reliable way to find the missing term. It may be slightly less efficient than the average method as it relies on an iterative comparison.
  • Method 5: List Comprehension with Enumeration. The one-liner is the most Pythonic, using features of the language to provide a compact solution. It’s best for developers comfortable with list comprehensions and generator expressions.
def find_missing_formula(seq):
    diff = (seq[-1] - seq[0]) // len(seq)
    for i, value in enumerate(seq):
        if value != seq[0] + i * diff:
            return seq[0] + i * diff
    return None

sequence = [3, 7, 11, 19]
missing_number = find_missing_formula(sequence)
print(f"The missing term is: {missing_number}")

The output of this code snippet:

The missing term is: 15

This snippet relies on the formula for an arithmetic sequence to deduce what each term should be. When it encounters a value in the sequence that doesn’t match the calculated value, it returns the expected value which corresponds to the missing term.

Bonus One-Liner Method 5: List Comprehension with Enumeration

This one-liner leverages list comprehension and the enumerate function in Python to quickly identify the missing term in an arithmetic sequence. It is a concise and Pythonic way of addressing the problem.

Here’s an example:

sequence = [3, 7, 15, 19]
diff = (sequence[-1] - sequence[0]) // len(sequence)
missing_number = next(sequence[0] + i * diff for i, num in enumerate(sequence) if num != sequence[0] + i * diff)
print(f"The missing term is: {missing_number}")

The output of this code snippet:

The missing term is: 11

This one-liner uses a generator expression with the next function to iterate over enumerated sequence items. It immediately returns the first missing term found without having to process the entire sequence.

Summary/Discussion

  • Method 1: Calculate Using Average. This method is straightforward and efficient, suitable for sequences where the first and last terms are known. However, it’s not applicable if the sequence is unordered or these terms are missing.
  • Method 2: Use Sequence Properties. This approach is methodical and does not require knowledge of all sequence terms, making it versatile. However, it is not the most efficient for very long sequences since it requires iterating through all terms until the missing one is found.
  • Method 3: Using Set Differences. It is intuitive and works well when the complete range of the sequence is known, but it can be less efficient with very large sequences due to the cost of creating sets.
  • Method 4: Leveraging Arithmetic Sequence Formula. This method is precise and follows a mathematical approach, which is a reliable way to find the missing term. It may be slightly less efficient than the average method as it relies on an iterative comparison.
  • Method 5: List Comprehension with Enumeration. The one-liner is the most Pythonic, using features of the language to provide a compact solution. It’s best for developers comfortable with list comprehensions and generator expressions.
def find_removed_term(seq):
    diff = (seq[-1] - seq[0]) // len(seq)
    for i in range(len(seq) - 1):
        if seq[i+1] - seq[i] != diff:
            return seq[i] + diff
    return None

sequence = [3, 7, 15, 19]
missing_number = find_removed_term(sequence)
print(f"Removed term: {missing_number}")

The output of this code snippet:

Removed term: 11

This snippet finds the expected common difference and then iterates through the provided sequence looking for the point where the difference between two terms does not match this expected difference. The missing term is then returned.

Method 3: Using Set Differences

The set difference method involves creating a complete set of numbers for the arithmetic sequence and then using set subtraction to find the missing term. This is an intuitive approach but requires knowledge of the common difference and the range of numbers.

Here’s an example:

def find_missing_set(seq, start, end, step):
    full_set = set(range(start, end + step, step))
    given_set = set(seq)
    missing = full_set - given_set
    return missing.pop() if missing else None

sequence = [3, 7, 15, 19]
missing_number = find_missing_set(sequence, 3, 19, 4)
print(f"The missing number is: {missing_number}")

The output of this code snippet:

The missing number is: 11

This code snippet creates a complete set from the beginning to end of where the sequence should span and then subtracts the set of the given sequence from it. The result is the set of missing numbers, from which the missing term can be extracted.

Method 4: Leveraging Arithmetic Sequence Formula

By using the arithmetic sequence formula \(a_n = a_1 + (n – 1) * d\), where \(a_n\) is the nth term, \(a_1\) is the first term, and \(d\) is the common difference, we can precisely calculate each term. Comparing the calculated terms against the given sequence, we can spot the removed term.

Here’s an example:

def find_missing_formula(seq):
    diff = (seq[-1] - seq[0]) // len(seq)
    for i, value in enumerate(seq):
        if value != seq[0] + i * diff:
            return seq[0] + i * diff
    return None

sequence = [3, 7, 11, 19]
missing_number = find_missing_formula(sequence)
print(f"The missing term is: {missing_number}")

The output of this code snippet:

The missing term is: 15

This snippet relies on the formula for an arithmetic sequence to deduce what each term should be. When it encounters a value in the sequence that doesn’t match the calculated value, it returns the expected value which corresponds to the missing term.

Bonus One-Liner Method 5: List Comprehension with Enumeration

This one-liner leverages list comprehension and the enumerate function in Python to quickly identify the missing term in an arithmetic sequence. It is a concise and Pythonic way of addressing the problem.

Here’s an example:

sequence = [3, 7, 15, 19]
diff = (sequence[-1] - sequence[0]) // len(sequence)
missing_number = next(sequence[0] + i * diff for i, num in enumerate(sequence) if num != sequence[0] + i * diff)
print(f"The missing term is: {missing_number}")

The output of this code snippet:

The missing term is: 11

This one-liner uses a generator expression with the next function to iterate over enumerated sequence items. It immediately returns the first missing term found without having to process the entire sequence.

Summary/Discussion

  • Method 1: Calculate Using Average. This method is straightforward and efficient, suitable for sequences where the first and last terms are known. However, it’s not applicable if the sequence is unordered or these terms are missing.
  • Method 2: Use Sequence Properties. This approach is methodical and does not require knowledge of all sequence terms, making it versatile. However, it is not the most efficient for very long sequences since it requires iterating through all terms until the missing one is found.
  • Method 3: Using Set Differences. It is intuitive and works well when the complete range of the sequence is known, but it can be less efficient with very large sequences due to the cost of creating sets.
  • Method 4: Leveraging Arithmetic Sequence Formula. This method is precise and follows a mathematical approach, which is a reliable way to find the missing term. It may be slightly less efficient than the average method as it relies on an iterative comparison.
  • Method 5: List Comprehension with Enumeration. The one-liner is the most Pythonic, using features of the language to provide a compact solution. It’s best for developers comfortable with list comprehensions and generator expressions.
def find_missing_set(seq, start, end, step):
    full_set = set(range(start, end + step, step))
    given_set = set(seq)
    missing = full_set - given_set
    return missing.pop() if missing else None

sequence = [3, 7, 15, 19]
missing_number = find_missing_set(sequence, 3, 19, 4)
print(f"The missing number is: {missing_number}")

The output of this code snippet:

The missing number is: 11

This code snippet creates a complete set from the beginning to end of where the sequence should span and then subtracts the set of the given sequence from it. The result is the set of missing numbers, from which the missing term can be extracted.

Method 4: Leveraging Arithmetic Sequence Formula

By using the arithmetic sequence formula \(a_n = a_1 + (n – 1) * d\), where \(a_n\) is the nth term, \(a_1\) is the first term, and \(d\) is the common difference, we can precisely calculate each term. Comparing the calculated terms against the given sequence, we can spot the removed term.

Here’s an example:

def find_missing_formula(seq):
    diff = (seq[-1] - seq[0]) // len(seq)
    for i, value in enumerate(seq):
        if value != seq[0] + i * diff:
            return seq[0] + i * diff
    return None

sequence = [3, 7, 11, 19]
missing_number = find_missing_formula(sequence)
print(f"The missing term is: {missing_number}")

The output of this code snippet:

The missing term is: 15

This snippet relies on the formula for an arithmetic sequence to deduce what each term should be. When it encounters a value in the sequence that doesn’t match the calculated value, it returns the expected value which corresponds to the missing term.

Bonus One-Liner Method 5: List Comprehension with Enumeration

This one-liner leverages list comprehension and the enumerate function in Python to quickly identify the missing term in an arithmetic sequence. It is a concise and Pythonic way of addressing the problem.

Here’s an example:

sequence = [3, 7, 15, 19]
diff = (sequence[-1] - sequence[0]) // len(sequence)
missing_number = next(sequence[0] + i * diff for i, num in enumerate(sequence) if num != sequence[0] + i * diff)
print(f"The missing term is: {missing_number}")

The output of this code snippet:

The missing term is: 11

This one-liner uses a generator expression with the next function to iterate over enumerated sequence items. It immediately returns the first missing term found without having to process the entire sequence.

Summary/Discussion

  • Method 1: Calculate Using Average. This method is straightforward and efficient, suitable for sequences where the first and last terms are known. However, it’s not applicable if the sequence is unordered or these terms are missing.
  • Method 2: Use Sequence Properties. This approach is methodical and does not require knowledge of all sequence terms, making it versatile. However, it is not the most efficient for very long sequences since it requires iterating through all terms until the missing one is found.
  • Method 3: Using Set Differences. It is intuitive and works well when the complete range of the sequence is known, but it can be less efficient with very large sequences due to the cost of creating sets.
  • Method 4: Leveraging Arithmetic Sequence Formula. This method is precise and follows a mathematical approach, which is a reliable way to find the missing term. It may be slightly less efficient than the average method as it relies on an iterative comparison.
  • Method 5: List Comprehension with Enumeration. The one-liner is the most Pythonic, using features of the language to provide a compact solution. It’s best for developers comfortable with list comprehensions and generator expressions.
def find_removed_term(seq):
    diff = (seq[-1] - seq[0]) // len(seq)
    for i in range(len(seq) - 1):
        if seq[i+1] - seq[i] != diff:
            return seq[i] + diff
    return None

sequence = [3, 7, 15, 19]
missing_number = find_removed_term(sequence)
print(f"Removed term: {missing_number}")

The output of this code snippet:

Removed term: 11

This snippet finds the expected common difference and then iterates through the provided sequence looking for the point where the difference between two terms does not match this expected difference. The missing term is then returned.

Method 3: Using Set Differences

The set difference method involves creating a complete set of numbers for the arithmetic sequence and then using set subtraction to find the missing term. This is an intuitive approach but requires knowledge of the common difference and the range of numbers.

Here’s an example:

def find_missing_set(seq, start, end, step):
    full_set = set(range(start, end + step, step))
    given_set = set(seq)
    missing = full_set - given_set
    return missing.pop() if missing else None

sequence = [3, 7, 15, 19]
missing_number = find_missing_set(sequence, 3, 19, 4)
print(f"The missing number is: {missing_number}")

The output of this code snippet:

The missing number is: 11

This code snippet creates a complete set from the beginning to end of where the sequence should span and then subtracts the set of the given sequence from it. The result is the set of missing numbers, from which the missing term can be extracted.

Method 4: Leveraging Arithmetic Sequence Formula

By using the arithmetic sequence formula \(a_n = a_1 + (n – 1) * d\), where \(a_n\) is the nth term, \(a_1\) is the first term, and \(d\) is the common difference, we can precisely calculate each term. Comparing the calculated terms against the given sequence, we can spot the removed term.

Here’s an example:

def find_missing_formula(seq):
    diff = (seq[-1] - seq[0]) // len(seq)
    for i, value in enumerate(seq):
        if value != seq[0] + i * diff:
            return seq[0] + i * diff
    return None

sequence = [3, 7, 11, 19]
missing_number = find_missing_formula(sequence)
print(f"The missing term is: {missing_number}")

The output of this code snippet:

The missing term is: 15

This snippet relies on the formula for an arithmetic sequence to deduce what each term should be. When it encounters a value in the sequence that doesn’t match the calculated value, it returns the expected value which corresponds to the missing term.

Bonus One-Liner Method 5: List Comprehension with Enumeration

This one-liner leverages list comprehension and the enumerate function in Python to quickly identify the missing term in an arithmetic sequence. It is a concise and Pythonic way of addressing the problem.

Here’s an example:

sequence = [3, 7, 15, 19]
diff = (sequence[-1] - sequence[0]) // len(sequence)
missing_number = next(sequence[0] + i * diff for i, num in enumerate(sequence) if num != sequence[0] + i * diff)
print(f"The missing term is: {missing_number}")

The output of this code snippet:

The missing term is: 11

This one-liner uses a generator expression with the next function to iterate over enumerated sequence items. It immediately returns the first missing term found without having to process the entire sequence.

Summary/Discussion

  • Method 1: Calculate Using Average. This method is straightforward and efficient, suitable for sequences where the first and last terms are known. However, it’s not applicable if the sequence is unordered or these terms are missing.
  • Method 2: Use Sequence Properties. This approach is methodical and does not require knowledge of all sequence terms, making it versatile. However, it is not the most efficient for very long sequences since it requires iterating through all terms until the missing one is found.
  • Method 3: Using Set Differences. It is intuitive and works well when the complete range of the sequence is known, but it can be less efficient with very large sequences due to the cost of creating sets.
  • Method 4: Leveraging Arithmetic Sequence Formula. This method is precise and follows a mathematical approach, which is a reliable way to find the missing term. It may be slightly less efficient than the average method as it relies on an iterative comparison.
  • Method 5: List Comprehension with Enumeration. The one-liner is the most Pythonic, using features of the language to provide a compact solution. It’s best for developers comfortable with list comprehensions and generator expressions.
def find_missing_formula(seq):
    diff = (seq[-1] - seq[0]) // len(seq)
    for i, value in enumerate(seq):
        if value != seq[0] + i * diff:
            return seq[0] + i * diff
    return None

sequence = [3, 7, 11, 19]
missing_number = find_missing_formula(sequence)
print(f"The missing term is: {missing_number}")

The output of this code snippet:

The missing term is: 15

This snippet relies on the formula for an arithmetic sequence to deduce what each term should be. When it encounters a value in the sequence that doesn’t match the calculated value, it returns the expected value which corresponds to the missing term.

Bonus One-Liner Method 5: List Comprehension with Enumeration

This one-liner leverages list comprehension and the enumerate function in Python to quickly identify the missing term in an arithmetic sequence. It is a concise and Pythonic way of addressing the problem.

Here’s an example:

sequence = [3, 7, 15, 19]
diff = (sequence[-1] - sequence[0]) // len(sequence)
missing_number = next(sequence[0] + i * diff for i, num in enumerate(sequence) if num != sequence[0] + i * diff)
print(f"The missing term is: {missing_number}")

The output of this code snippet:

The missing term is: 11

This one-liner uses a generator expression with the next function to iterate over enumerated sequence items. It immediately returns the first missing term found without having to process the entire sequence.

Summary/Discussion

  • Method 1: Calculate Using Average. This method is straightforward and efficient, suitable for sequences where the first and last terms are known. However, it’s not applicable if the sequence is unordered or these terms are missing.
  • Method 2: Use Sequence Properties. This approach is methodical and does not require knowledge of all sequence terms, making it versatile. However, it is not the most efficient for very long sequences since it requires iterating through all terms until the missing one is found.
  • Method 3: Using Set Differences. It is intuitive and works well when the complete range of the sequence is known, but it can be less efficient with very large sequences due to the cost of creating sets.
  • Method 4: Leveraging Arithmetic Sequence Formula. This method is precise and follows a mathematical approach, which is a reliable way to find the missing term. It may be slightly less efficient than the average method as it relies on an iterative comparison.
  • Method 5: List Comprehension with Enumeration. The one-liner is the most Pythonic, using features of the language to provide a compact solution. It’s best for developers comfortable with list comprehensions and generator expressions.
def find_missing_set(seq, start, end, step):
    full_set = set(range(start, end + step, step))
    given_set = set(seq)
    missing = full_set - given_set
    return missing.pop() if missing else None

sequence = [3, 7, 15, 19]
missing_number = find_missing_set(sequence, 3, 19, 4)
print(f"The missing number is: {missing_number}")

The output of this code snippet:

The missing number is: 11

This code snippet creates a complete set from the beginning to end of where the sequence should span and then subtracts the set of the given sequence from it. The result is the set of missing numbers, from which the missing term can be extracted.

Method 4: Leveraging Arithmetic Sequence Formula

By using the arithmetic sequence formula \(a_n = a_1 + (n – 1) * d\), where \(a_n\) is the nth term, \(a_1\) is the first term, and \(d\) is the common difference, we can precisely calculate each term. Comparing the calculated terms against the given sequence, we can spot the removed term.

Here’s an example:

def find_missing_formula(seq):
    diff = (seq[-1] - seq[0]) // len(seq)
    for i, value in enumerate(seq):
        if value != seq[0] + i * diff:
            return seq[0] + i * diff
    return None

sequence = [3, 7, 11, 19]
missing_number = find_missing_formula(sequence)
print(f"The missing term is: {missing_number}")

The output of this code snippet:

The missing term is: 15

This snippet relies on the formula for an arithmetic sequence to deduce what each term should be. When it encounters a value in the sequence that doesn’t match the calculated value, it returns the expected value which corresponds to the missing term.

Bonus One-Liner Method 5: List Comprehension with Enumeration

This one-liner leverages list comprehension and the enumerate function in Python to quickly identify the missing term in an arithmetic sequence. It is a concise and Pythonic way of addressing the problem.

Here’s an example:

sequence = [3, 7, 15, 19]
diff = (sequence[-1] - sequence[0]) // len(sequence)
missing_number = next(sequence[0] + i * diff for i, num in enumerate(sequence) if num != sequence[0] + i * diff)
print(f"The missing term is: {missing_number}")

The output of this code snippet:

The missing term is: 11

This one-liner uses a generator expression with the next function to iterate over enumerated sequence items. It immediately returns the first missing term found without having to process the entire sequence.

Summary/Discussion

  • Method 1: Calculate Using Average. This method is straightforward and efficient, suitable for sequences where the first and last terms are known. However, it’s not applicable if the sequence is unordered or these terms are missing.
  • Method 2: Use Sequence Properties. This approach is methodical and does not require knowledge of all sequence terms, making it versatile. However, it is not the most efficient for very long sequences since it requires iterating through all terms until the missing one is found.
  • Method 3: Using Set Differences. It is intuitive and works well when the complete range of the sequence is known, but it can be less efficient with very large sequences due to the cost of creating sets.
  • Method 4: Leveraging Arithmetic Sequence Formula. This method is precise and follows a mathematical approach, which is a reliable way to find the missing term. It may be slightly less efficient than the average method as it relies on an iterative comparison.
  • Method 5: List Comprehension with Enumeration. The one-liner is the most Pythonic, using features of the language to provide a compact solution. It’s best for developers comfortable with list comprehensions and generator expressions.
def find_removed_term(seq):
    diff = (seq[-1] - seq[0]) // len(seq)
    for i in range(len(seq) - 1):
        if seq[i+1] - seq[i] != diff:
            return seq[i] + diff
    return None

sequence = [3, 7, 15, 19]
missing_number = find_removed_term(sequence)
print(f"Removed term: {missing_number}")

The output of this code snippet:

Removed term: 11

This snippet finds the expected common difference and then iterates through the provided sequence looking for the point where the difference between two terms does not match this expected difference. The missing term is then returned.

Method 3: Using Set Differences

The set difference method involves creating a complete set of numbers for the arithmetic sequence and then using set subtraction to find the missing term. This is an intuitive approach but requires knowledge of the common difference and the range of numbers.

Here’s an example:

def find_missing_set(seq, start, end, step):
    full_set = set(range(start, end + step, step))
    given_set = set(seq)
    missing = full_set - given_set
    return missing.pop() if missing else None

sequence = [3, 7, 15, 19]
missing_number = find_missing_set(sequence, 3, 19, 4)
print(f"The missing number is: {missing_number}")

The output of this code snippet:

The missing number is: 11

This code snippet creates a complete set from the beginning to end of where the sequence should span and then subtracts the set of the given sequence from it. The result is the set of missing numbers, from which the missing term can be extracted.

Method 4: Leveraging Arithmetic Sequence Formula

By using the arithmetic sequence formula \(a_n = a_1 + (n – 1) * d\), where \(a_n\) is the nth term, \(a_1\) is the first term, and \(d\) is the common difference, we can precisely calculate each term. Comparing the calculated terms against the given sequence, we can spot the removed term.

Here’s an example:

def find_missing_formula(seq):
    diff = (seq[-1] - seq[0]) // len(seq)
    for i, value in enumerate(seq):
        if value != seq[0] + i * diff:
            return seq[0] + i * diff
    return None

sequence = [3, 7, 11, 19]
missing_number = find_missing_formula(sequence)
print(f"The missing term is: {missing_number}")

The output of this code snippet:

The missing term is: 15

This snippet relies on the formula for an arithmetic sequence to deduce what each term should be. When it encounters a value in the sequence that doesn’t match the calculated value, it returns the expected value which corresponds to the missing term.

Bonus One-Liner Method 5: List Comprehension with Enumeration

This one-liner leverages list comprehension and the enumerate function in Python to quickly identify the missing term in an arithmetic sequence. It is a concise and Pythonic way of addressing the problem.

Here’s an example:

sequence = [3, 7, 15, 19]
diff = (sequence[-1] - sequence[0]) // len(sequence)
missing_number = next(sequence[0] + i * diff for i, num in enumerate(sequence) if num != sequence[0] + i * diff)
print(f"The missing term is: {missing_number}")

The output of this code snippet:

The missing term is: 11

This one-liner uses a generator expression with the next function to iterate over enumerated sequence items. It immediately returns the first missing term found without having to process the entire sequence.

Summary/Discussion

  • Method 1: Calculate Using Average. This method is straightforward and efficient, suitable for sequences where the first and last terms are known. However, it’s not applicable if the sequence is unordered or these terms are missing.
  • Method 2: Use Sequence Properties. This approach is methodical and does not require knowledge of all sequence terms, making it versatile. However, it is not the most efficient for very long sequences since it requires iterating through all terms until the missing one is found.
  • Method 3: Using Set Differences. It is intuitive and works well when the complete range of the sequence is known, but it can be less efficient with very large sequences due to the cost of creating sets.
  • Method 4: Leveraging Arithmetic Sequence Formula. This method is precise and follows a mathematical approach, which is a reliable way to find the missing term. It may be slightly less efficient than the average method as it relies on an iterative comparison.
  • Method 5: List Comprehension with Enumeration. The one-liner is the most Pythonic, using features of the language to provide a compact solution. It’s best for developers comfortable with list comprehensions and generator expressions.

💡 Problem Formulation: The task is to identify the missing term from an incomplete arithmetic sequence. Suppose you have a list representing an arithmetic sequence with one term removed, the goal is to write a Python program that can find and return this missing number. For instance, if given [3, 7, 11, 19], with a common difference of 4, the removed term is 15.

Method 1: Calculate Using Average

This method computes the expected sum of a full sequence by multiplying the average of the first and last terms by the count of terms, including the missing one. By subtracting the sum of the given sequence from this calculated sum, the missing term can be deduced. It’s a straightforward and efficient approach when the first and last terms are known.

Here’s an example:

def find_missing(lst):
    n = len(lst) + 1
    expected_sum = (lst[0] + lst[-1]) * n // 2
    actual_sum = sum(lst)
    return expected_sum - actual_sum

sequence = [3, 7, 11, 19]
missing_number = find_missing(sequence)
print(f"The missing term is: {missing_number}")

The output of this code snippet:

The missing term is: 15

This code snippet works by calculating what the sum of the arithmetic sequence should be if it were complete. It finds the difference between this expected sum and the actual sum of the given sequence, which reveals the missing number.

Method 2: Use Sequence Properties

In an arithmetic sequence, the common difference is constant. By finding the difference between consecutive elements, inconsistencies can be noticed, and the missing term can be located. This method iteratively checks for the break in the pattern to identify the removed term.

Here’s an example:

sequence = [3, 7, 15, 19]
diff = (sequence[-1] - sequence[0]) // len(sequence)
missing_number = next(sequence[0] + i * diff for i, num in enumerate(sequence) if num != sequence[0] + i * diff)
print(f"The missing term is: {missing_number}")

The output of this code snippet:

The missing term is: 11

This one-liner uses a generator expression with the next function to iterate over enumerated sequence items. It immediately returns the first missing term found without having to process the entire sequence.

Summary/Discussion

  • Method 1: Calculate Using Average. This method is straightforward and efficient, suitable for sequences where the first and last terms are known. However, it’s not applicable if the sequence is unordered or these terms are missing.
  • Method 2: Use Sequence Properties. This approach is methodical and does not require knowledge of all sequence terms, making it versatile. However, it is not the most efficient for very long sequences since it requires iterating through all terms until the missing one is found.
  • Method 3: Using Set Differences. It is intuitive and works well when the complete range of the sequence is known, but it can be less efficient with very large sequences due to the cost of creating sets.
  • Method 4: Leveraging Arithmetic Sequence Formula. This method is precise and follows a mathematical approach, which is a reliable way to find the missing term. It may be slightly less efficient than the average method as it relies on an iterative comparison.
  • Method 5: List Comprehension with Enumeration. The one-liner is the most Pythonic, using features of the language to provide a compact solution. It’s best for developers comfortable with list comprehensions and generator expressions.
def find_missing_formula(seq):
    diff = (seq[-1] - seq[0]) // len(seq)
    for i, value in enumerate(seq):
        if value != seq[0] + i * diff:
            return seq[0] + i * diff
    return None

sequence = [3, 7, 11, 19]
missing_number = find_missing_formula(sequence)
print(f"The missing term is: {missing_number}")

The output of this code snippet:

The missing term is: 15

This snippet relies on the formula for an arithmetic sequence to deduce what each term should be. When it encounters a value in the sequence that doesn’t match the calculated value, it returns the expected value which corresponds to the missing term.

Bonus One-Liner Method 5: List Comprehension with Enumeration

This one-liner leverages list comprehension and the enumerate function in Python to quickly identify the missing term in an arithmetic sequence. It is a concise and Pythonic way of addressing the problem.

Here’s an example:

sequence = [3, 7, 15, 19]
diff = (sequence[-1] - sequence[0]) // len(sequence)
missing_number = next(sequence[0] + i * diff for i, num in enumerate(sequence) if num != sequence[0] + i * diff)
print(f"The missing term is: {missing_number}")

The output of this code snippet:

The missing term is: 11

This one-liner uses a generator expression with the next function to iterate over enumerated sequence items. It immediately returns the first missing term found without having to process the entire sequence.

Summary/Discussion

  • Method 1: Calculate Using Average. This method is straightforward and efficient, suitable for sequences where the first and last terms are known. However, it’s not applicable if the sequence is unordered or these terms are missing.
  • Method 2: Use Sequence Properties. This approach is methodical and does not require knowledge of all sequence terms, making it versatile. However, it is not the most efficient for very long sequences since it requires iterating through all terms until the missing one is found.
  • Method 3: Using Set Differences. It is intuitive and works well when the complete range of the sequence is known, but it can be less efficient with very large sequences due to the cost of creating sets.
  • Method 4: Leveraging Arithmetic Sequence Formula. This method is precise and follows a mathematical approach, which is a reliable way to find the missing term. It may be slightly less efficient than the average method as it relies on an iterative comparison.
  • Method 5: List Comprehension with Enumeration. The one-liner is the most Pythonic, using features of the language to provide a compact solution. It’s best for developers comfortable with list comprehensions and generator expressions.
def find_missing_set(seq, start, end, step):
    full_set = set(range(start, end + step, step))
    given_set = set(seq)
    missing = full_set - given_set
    return missing.pop() if missing else None

sequence = [3, 7, 15, 19]
missing_number = find_missing_set(sequence, 3, 19, 4)
print(f"The missing number is: {missing_number}")

The output of this code snippet:

The missing number is: 11

This code snippet creates a complete set from the beginning to end of where the sequence should span and then subtracts the set of the given sequence from it. The result is the set of missing numbers, from which the missing term can be extracted.

Method 4: Leveraging Arithmetic Sequence Formula

By using the arithmetic sequence formula \(a_n = a_1 + (n – 1) * d\), where \(a_n\) is the nth term, \(a_1\) is the first term, and \(d\) is the common difference, we can precisely calculate each term. Comparing the calculated terms against the given sequence, we can spot the removed term.

Here’s an example:

def find_missing_formula(seq):
    diff = (seq[-1] - seq[0]) // len(seq)
    for i, value in enumerate(seq):
        if value != seq[0] + i * diff:
            return seq[0] + i * diff
    return None

sequence = [3, 7, 11, 19]
missing_number = find_missing_formula(sequence)
print(f"The missing term is: {missing_number}")

The output of this code snippet:

The missing term is: 15

This snippet relies on the formula for an arithmetic sequence to deduce what each term should be. When it encounters a value in the sequence that doesn’t match the calculated value, it returns the expected value which corresponds to the missing term.

Bonus One-Liner Method 5: List Comprehension with Enumeration

This one-liner leverages list comprehension and the enumerate function in Python to quickly identify the missing term in an arithmetic sequence. It is a concise and Pythonic way of addressing the problem.

Here’s an example:

sequence = [3, 7, 15, 19]
diff = (sequence[-1] - sequence[0]) // len(sequence)
missing_number = next(sequence[0] + i * diff for i, num in enumerate(sequence) if num != sequence[0] + i * diff)
print(f"The missing term is: {missing_number}")

The output of this code snippet:

The missing term is: 11

This one-liner uses a generator expression with the next function to iterate over enumerated sequence items. It immediately returns the first missing term found without having to process the entire sequence.

Summary/Discussion

  • Method 1: Calculate Using Average. This method is straightforward and efficient, suitable for sequences where the first and last terms are known. However, it’s not applicable if the sequence is unordered or these terms are missing.
  • Method 2: Use Sequence Properties. This approach is methodical and does not require knowledge of all sequence terms, making it versatile. However, it is not the most efficient for very long sequences since it requires iterating through all terms until the missing one is found.
  • Method 3: Using Set Differences. It is intuitive and works well when the complete range of the sequence is known, but it can be less efficient with very large sequences due to the cost of creating sets.
  • Method 4: Leveraging Arithmetic Sequence Formula. This method is precise and follows a mathematical approach, which is a reliable way to find the missing term. It may be slightly less efficient than the average method as it relies on an iterative comparison.
  • Method 5: List Comprehension with Enumeration. The one-liner is the most Pythonic, using features of the language to provide a compact solution. It’s best for developers comfortable with list comprehensions and generator expressions.
def find_removed_term(seq):
    diff = (seq[-1] - seq[0]) // len(seq)
    for i in range(len(seq) - 1):
        if seq[i+1] - seq[i] != diff:
            return seq[i] + diff
    return None

sequence = [3, 7, 15, 19]
missing_number = find_removed_term(sequence)
print(f"Removed term: {missing_number}")

The output of this code snippet:

Removed term: 11

This snippet finds the expected common difference and then iterates through the provided sequence looking for the point where the difference between two terms does not match this expected difference. The missing term is then returned.

Method 3: Using Set Differences

The set difference method involves creating a complete set of numbers for the arithmetic sequence and then using set subtraction to find the missing term. This is an intuitive approach but requires knowledge of the common difference and the range of numbers.

Here’s an example:

def find_missing_set(seq, start, end, step):
    full_set = set(range(start, end + step, step))
    given_set = set(seq)
    missing = full_set - given_set
    return missing.pop() if missing else None

sequence = [3, 7, 15, 19]
missing_number = find_missing_set(sequence, 3, 19, 4)
print(f"The missing number is: {missing_number}")

The output of this code snippet:

The missing number is: 11

This code snippet creates a complete set from the beginning to end of where the sequence should span and then subtracts the set of the given sequence from it. The result is the set of missing numbers, from which the missing term can be extracted.

Method 4: Leveraging Arithmetic Sequence Formula

By using the arithmetic sequence formula \(a_n = a_1 + (n – 1) * d\), where \(a_n\) is the nth term, \(a_1\) is the first term, and \(d\) is the common difference, we can precisely calculate each term. Comparing the calculated terms against the given sequence, we can spot the removed term.

Here’s an example:

def find_missing_formula(seq):
    diff = (seq[-1] - seq[0]) // len(seq)
    for i, value in enumerate(seq):
        if value != seq[0] + i * diff:
            return seq[0] + i * diff
    return None

sequence = [3, 7, 11, 19]
missing_number = find_missing_formula(sequence)
print(f"The missing term is: {missing_number}")

The output of this code snippet:

The missing term is: 15

This snippet relies on the formula for an arithmetic sequence to deduce what each term should be. When it encounters a value in the sequence that doesn’t match the calculated value, it returns the expected value which corresponds to the missing term.

Bonus One-Liner Method 5: List Comprehension with Enumeration

This one-liner leverages list comprehension and the enumerate function in Python to quickly identify the missing term in an arithmetic sequence. It is a concise and Pythonic way of addressing the problem.

Here’s an example:

sequence = [3, 7, 15, 19]
diff = (sequence[-1] - sequence[0]) // len(sequence)
missing_number = next(sequence[0] + i * diff for i, num in enumerate(sequence) if num != sequence[0] + i * diff)
print(f"The missing term is: {missing_number}")

The output of this code snippet:

The missing term is: 11

This one-liner uses a generator expression with the next function to iterate over enumerated sequence items. It immediately returns the first missing term found without having to process the entire sequence.

Summary/Discussion

  • Method 1: Calculate Using Average. This method is straightforward and efficient, suitable for sequences where the first and last terms are known. However, it’s not applicable if the sequence is unordered or these terms are missing.
  • Method 2: Use Sequence Properties. This approach is methodical and does not require knowledge of all sequence terms, making it versatile. However, it is not the most efficient for very long sequences since it requires iterating through all terms until the missing one is found.
  • Method 3: Using Set Differences. It is intuitive and works well when the complete range of the sequence is known, but it can be less efficient with very large sequences due to the cost of creating sets.
  • Method 4: Leveraging Arithmetic Sequence Formula. This method is precise and follows a mathematical approach, which is a reliable way to find the missing term. It may be slightly less efficient than the average method as it relies on an iterative comparison.
  • Method 5: List Comprehension with Enumeration. The one-liner is the most Pythonic, using features of the language to provide a compact solution. It’s best for developers comfortable with list comprehensions and generator expressions.