Geometric Sequence Calculator

The Geometric Sequence Calculator is a free online tool that instantly computes the nth term, sum, and infinite sum of a geometric sequence from the first term (a1), common ratio (r), and number of terms (n).

What Is a Geometric Sequence?

A geometric sequence is a series of numbers where the ratio between any two consecutive terms is constant. For example, "2, 6, 18, 54, …" is a geometric sequence with first term 2 and common ratio 3. The nth term is calculated as a_n = a1 × r^(n-1). The sum of the first n terms is S_n = a1(1 - r^n)/(1 - r) when r ≠ 1, or S_n = a1 × n when r = 1. For |r| < 1, the infinite series converges to S_∞ = a1/(1 - r).

What This Tool Does

- Automatically calculates the nth term (a_n) value - Computes the sum of all terms from a1 through a_n (S_n) - Displays the infinite sum S_∞ when |r| < 1 - Shows the general term formula and your specific calculation - Lists sequence terms up to 50 items (displays first 10 and last 10 for n > 50) - Handles very large or very small values using exponential notation - Supports decimals, negative ratios, and r = 0

Who Is This For?

- High school and university students studying geometric progressions and series - Exam takers preparing for entrance exams or mathematics certification tests - Professionals verifying compound interest, population growth, radioactive decay, and other real-world geometric applications - Engineers and programmers generating or validating geometric sequence data

All calculations run entirely in your browser — no data is sent to any server. No installation or account required; works on desktop and mobile devices alike.