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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(100)
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(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 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(6)
print(result)

1 answer

To calculate the sum of the first 6 terms in the sequence \(7n + 1\), you would want to alter the sum function accordingly. Here’s how it can be done correctly:

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

result = sum(6)
print(result)

This code will correctly calculate the sum of the first 6 terms of the series \(7n + 1\) where \(n\) runs from 1 to 6.

To clarify what happens here:

  • When \(n = 6\), it calculates \(7*6 + 1\).
  • It then calls itself with \(n = 5\), \(7*5 + 1\), and so forth until it reaches \(n = 1\) and finally \(n = 0\) (which returns 0 and ends the recursion).

The output of this code will sum up all the values \(71 + 1\), \(72 + 1\), \(73 + 1\), \(74 + 1\), \(75 + 1\), and \(76 + 1\).