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 10 numbers in the sequence 3n−1?
(1 point)
Responses

def sum(n):
if n == 0:
return 0
else:
return 3 * n - 1 + sum(n - 1)
result = sum(100)
print(result)
def sum(n): if n == 0: return 0 else: return 3 * n - 1 + sum(n - 1) result = sum(100) print(result)

def sum(n):
if n == 0:
return 0
else:
return 3 * n - 1 + sum(n - 1)
result = sum(10)
print(result)
def sum(n): if n == 0: return 0 else: return 3 * n - 1 + sum(n - 1) result = sum(10) print(result)

def sum(n):
if n == 0:
return 0
else:
return 3 * (n - 1) + sum(n - 1)
result = sum(10)
print(result)
def sum(n): if n == 0: return 0 else: return 3 * (n - 1) + sum(n - 1) result = sum(10) print(result)

def sum(n):
if n <= 0:
return 0
else:
return n + sum(3 * n - 1)
result = sum(10)
print(result)

Answer 1

To alter the provided recursive function to calculate the sum of the first 10 numbers in the sequence defined by the formula \(3n - 1\), we need to ensure that we call the function with \(n = 10\) and modify the function so that it correctly computes the sum based on the formula.

The correct response from your options would be:

```python
def sum(n):
if n == 0:
return 0
else:
return 3 * n - 1 + sum(n - 1)
result = sum(10)
print(result)
```

Here's why this is the correct choice:

- The function `sum(n)` appropriately calculates the sum of \(3n - 1\) for each \(n\) from \(1\) to \(10\).
- The base case checks if \(n\) is \(0\) (in which case it returns \(0\), as there are no numbers to sum), and the recursive case computes \(3n - 1\) and adds it to the sum of the previous numbers (by calling `sum(n - 1)`).
- Finally, `result = sum(10)` calls the modified sum function to compute the desired sum for the first 10 numbers in the sequence.

The other options either contain incorrect logic or would not produce the correct result based on your requirement.