calculating arithmetic progression with recursion

Question

I'm trying to make a function that is given the first number in an arithmetic progression, the derivation d and the number of terms in the series which is n and then calculate their sum using recursion I tried the following

def rec_sum(a_1, d, n):
    if n == 0:
        return 0

    return (n*(a_1+rec_sum(a_1,d,n-1)))/2

print rec_sum(2,2,4)

which gives me 18 instead of 20 thanks for the help

Answer 1

There is a simpler way to find the sum of arithmetic progression, but if you need the recursion -

def rec_sum(first_element, step, seq_length):
    if seq_length <= 0:
        return 0
    return first_element + rec_sum(first_element + step, step, seq_length - 1)

Answer 2

Another solution:

def rec_sum(a_1, d, n):
    if n == 0:
        return 0
    return a_1 + rec_sum(a_1 + d, d, n-1)

print rec_sum(2, 2, 4)

output:

20