Geometric Sequence Calculator

In compound interest, population growth, radioactive decay, and computer algorithms such as binary search analysis.

First term — the starting value of the sequence.
Common ratio — the number each term is multiplied by. It can be negative, fractional or greater than 1.
Term number — which term to display, plus how many terms to sum.

Frequently Asked Questions

What is a geometric sequence?

A sequence where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

What is an example?

2, 6, 18, 54 … has a common ratio of 3. Each term is the previous one times 3.

When does the infinite sum converge?

Only when the absolute value of the ratio is less than 1 (|r| < 1). Otherwise the terms grow without bound and the infinite sum diverges.

Where are geometric sequences used?

In compound interest, population growth, radioactive decay, and computer algorithms such as binary search analysis.

The sequence starting at 3 with ratio 2:

How to Use This Calculator