Geometric Sequence Calculator

About this calculator

This calculator finds the nth term and the sum of a geometric sequence — a list of numbers where each term is found by multiplying the previous one by a fixed common ratio — using the first term and that common ratio as inputs. Unlike an arithmetic sequence, which grows by a constant amount, a geometric sequence grows (or shrinks) by a constant multiplying factor, which produces either accelerating growth or decay depending on whether the ratio is greater or less than 1.

It's a standard topic in algebra and pre-calculus coursework, where students compute specific terms and partial sums to understand exponential patterns. Beyond the classroom, the same structure models real phenomena with multiplicative, compounding growth or decline: compound interest growing a balance by a fixed percentage each period, population or bacterial growth under ideal conditions, and radioactive decay or depreciation, where a fixed fraction is lost at each step rather than a fixed amount.