Geometric Series Sum

Problem

Given first term a, integer ratio r and a count n, return [nth term, sum of the first n terms].

The nth term is a * r ** (n - 1); for r != 1 the sum is a * (r ** n - 1) // (r - 1), and for r == 1 it is a * n. Assume n >= 1 and integer arithmetic.

Hint

The closed form divides exactly for integer geometric series with r != 1.

Test cases

case 1

in: [1,2,4]

expected: [8,15]

case 2

in: [2,3,3]

expected: [18,26]

case 3

in: [5,1,4]

expected: [5,20]

case 4

in: [0,7,5]

expected: [0,0]

case 5

in: [3,-1,4]

expected: [-3,0]

Starter codePython

def geometric_series(a, r, n):
    # Your code here
    pass

5 test cases · run your code against them in the editor