Geometric Sequence Calculator for the Nth Term, Finite Sum and Infinite Sum

Updated By Unit Conversion Plus

Find the nth term and sum of a geometric sequence, including a convergent infinite sum.

Enter the sequence

What is a geometric sequence?

Each term in a geometric sequence is found by multiplying the previous term by a fixed common ratio.

aₙ = a₁rⁿ⁻¹
Sₙ = a₁(1 − rⁿ) ÷ (1 − r)

Geometric sequence example

For 2, 6, 18, 54, … the first term is 2 and the common ratio is 3. The sixth term is 486.

When does an infinite sum exist?

An infinite geometric series converges only when the absolute value of the common ratio is less than 1. Its sum is a₁ ÷ (1 − r).

Frequently asked questions

How do I find the common ratio?

Divide a term by the non-zero term immediately before it.

What happens when the ratio is 1?

Every term equals the first term, so the sum of n terms is n times the first term.