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 ?
To alter the code to print the sum of the first 6 terms in the sequence 7n + 1, you would need to modify the recursive function `sum(n)` to calculate the desired sequence and update the variable `result` accordingly. Here's the modified code:
```
def sum(n):
if n < 1:
return 0
else:
return (7 * n) + 1 + sum(n - 1)
result = sum(6) # Calculating the sum of the first 6 terms
print(result)
```
In this modified code, the `sum(n)` function calculates the sum of the sequence 7n + 1. Each recursive call adds the current value of 7n + 1 to the sum of the previous terms until `n` becomes less than 1. Finally, the variable `result` stores the sum of the first 6 terms in the sequence, and it is printed to the console.
To alter the code to print the sum of the first 6 terms in the sequence 7n + 1, you can modify the recursive algorithm as follows:
```python
def sum_sequence(n):
if n < 1:
return 0
else:
return (7 * n + 1) + sum_sequence(n - 1)
result = sum_sequence(6)
print(result)
```
In this modified code, the `sum_sequence` function takes an input `n` and calculates the sum of the first `n` terms in the sequence 7n + 1 recursively. It utilizes the same base case as before (`n < 1` returns 0), and in the recursive step, it calculates the current term in the sequence using `7 * n + 1` and adds it to the sum of the remaining terms (`sum_sequence(n - 1)`).
By calling `sum_sequence(6)`, you calculate the sum of the first 6 terms in the sequence, and the result is printed.
To alter the code to print the sum of the first 6 terms in the sequence 7n + 1, you would need to modify the sum() function and the parameter passed to it. Here's how you can do it:
1. Define a new function named sum_sequence() that takes a parameter n representing the number of terms you want to sum.
2. Inside the sum_sequence() function, modify the base case (if condition) to check if n < 1 instead of n < 1.
3. Modify the recursive case (else condition) to calculate the next term in the sequence using the formula 7n + 1, and recursively call sum_sequence() with n - 1.
4. Update the function call in the line "result = sum(100)" to use the new function "sum_sequence" instead.
Here's the modified code:
```python
def sum_sequence(n):
if n < 1:
return 0
else:
term = 7 * n + 1
return term + sum_sequence(n - 1)
result = sum_sequence(6) # Calculates sum of the first 6 terms in the sequence
print(result)
```
When you run this code, it will print the sum of the first 6 terms in the sequence 7n + 1, which is the desired output.