Skip to content
Calculation Machine

Geometric Sequence Calculator

nth term and sum of a geometric series.

Reviewed by the Calculation Machine team · How we check our maths

Your values

ⓘ Live results

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).

The formula

aₙ = a₁r^(n−1), Sₙ = a₁(1−rⁿ)/(1−r)

Worked example

Worked example

Using the values the calculator loads with.

Inputs

  • First term3
  • Common ratio2
  • Term number10

Result

  • Term 101536
  • Sum of first n terms3069
  • Infinite sumDiverges
  • Common ratio2
  • First terms3, 6, 12, 24, 48, 96, 192, 384

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.

About this calculator