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 ?

Answer 1

To modify the given recursive algorithm to print the sum of the first 10 numbers in the sequence defined by the formula \(3n - 1\), we can follow these steps:

1. Change the base case to fit the new requirement.
2. Modify the recursive call to compute the sequence \(3n - 1\).

Here's the modified code:

```python
def sum_sequence(n, count=1):
if count > n: # Stop when we have summed n terms
return 0
else:
# Calculate the current term using the formula 3 * count - 1
return (3 * count - 1) + sum_sequence(n, count + 1) # Increment count

result = sum_sequence(10) # We want the sum of the first 10 terms
print(result)
```

### Explanation:
- The `sum_sequence` function now takes two parameters:
- `n`: The total number of terms to sum.
- `count`: Keeps track of how many terms have been summed so far (default starts at 1).
- The base case checks if `count` exceeds `n`, in which case it returns 0, ending the recursion.
- The recursive case computes the term \(3 \times \text{count} - 1\) and adds it to the recursive result of `sum_sequence` with `count` incremented by 1.

When this code is run, it will calculate and print the sum of the first 10 numbers of the sequence defined by \(3n - 1\).