Question

Given the code for the recursive algorithm that sums the sequence of numbers from one to one hundred: def sum(n): if n < 1: return 0 else: return n + sum(n - 1) result = sum(100) print(result) How could the code be altered to print the sum of the first 6 terms in the sequence, 7n+1? (1 point) Responses def sum(n): if n == 0: return 0 else: return 7 * n + 1 + sum(n - 1) result = sum(6) print(result) def sum(n): if n == 0: return 0 else: return 7 * n + 1 + sum(n - 1) result = sum(6) print(result) def sum(n): if n <= 0: return 0 else: return n + sum(7 * n - 6) result = sum(6) print(result) def sum(n): if n <= 0: return 0 else: return n + sum(7 * n - 6) result = sum(6) print(result) def sum(n): if n == 0: return 0 else: return 7 * n + 1 + sum(n - 1) result = sum(10) print(result) def sum(n): if n == 0: return 0 else: return 7 * n + 1 + sum(n - 1) result = sum(10) print(result) def sum(n): if n == 0: return 0 else: return 7 * n + 1 + sum(n - 1) result = sum(100) print(result) def sum(n): if n == 0: return 0 else: return 7 * n + 1 + sum(n - 1) result = sum(100) print(result) Skip to navigation

Answer 1

To alter the original recursive algorithm to compute the sum of the first 6 terms in the sequence given by the formula \(7n + 1\), the correct modification must build on the recursion structure but replace the function body to yield \(7n + 1\) for \(n\) ranging from 1 to 6.

The correct code would be:

def sum(n):
    if n == 0:
        return 0
    else:
        return 7 * n + 1 + sum(n - 1)

result = sum(6)
print(result)

This code correctly calculates the sum for \(n\) from 1 to 6 by evaluating \(7n + 1\) and accumulating the result in the recursion, which matches the pattern you’re looking for.

None of the provided incorrect options correctly instantiate the formula or the summation limit of \(n\) as 6. The alternatives you provided either reference summation beyond \(n = 6\), or use incorrect conditions. Hence, only this specific response is valid and should yield the correct sum of the first 6 terms in the \(7n + 1\) sequence (which would be the values when \(n = 1, 2, 3, 4, 5, 6\)).

If you were to calculate manually:

• For \(n=1\): \(7(1) + 1 = 8\)
• For \(n=2\): \(7(2) + 1 = 15\)
• For \(n=3\): \(7(3) + 1 = 22\)
• For \(n=4\): \(7(4) + 1 = 29\)
• For \(n=5\): \(7(5) + 1 = 36\)
• For \(n=6\): \(7(6) + 1 = 43\)

The total sum would be \(8 + 15 + 22 + 29 + 36 + 43 = 153\).