Geometric Series Sum Calculator

About this calculator

The sum of a finite geometric series — a sequence where each term is multiplied by a constant common ratio r — is given by Sn = a × (1 − r^n) divided by (1 − r), where a is the first term and n is the number of terms; unlike an arithmetic series, the terms of a geometric series can grow explosively when the ratio is greater than 1, or shrink toward zero when the ratio is between 0 and 1.

Geometric series model compound growth and decay throughout finance and science — compound interest and investment growth, population or bacterial growth models, radioactive decay chains, the depreciation of an asset's value by a fixed percentage each year, and the branching pattern of a chain letter or referral program all follow the same underlying formula.

This calculator takes the first term, common ratio, and number of terms and instantly returns the total sum of the series, working for both growing and shrinking sequences.