Math

Geometric Sequence Calculator

nth term and sum of a geometric series.

Enter your values

Results update instantly as you type — no submit needed.

Results
Term 10
1536
Sum of first n terms
3069
Infinite sum
Diverges
Common ratio
2
First terms
3, 6, 12, 24, 48, 96, 192, 384

Quick answer

Each geometric term multiplies the previous by a constant ratio r, so aₙ = a₁r^(n−1).

aₙ = a₁r^(n−1), Sₙ = a₁(1−rⁿ)/(1−r)

How to use the Geometric Sequence Calculator

  1. 1Enter the first term.
  2. 2Enter the common ratio between terms.
  3. 3Enter the term number you need.

Frequently asked questions

When does an infinite series converge?

Only when |r| < 1.

Can the ratio be negative?

Yes — the terms then alternate in sign.