Geometric Sequence Calculator
nth term and sum of a geometric series.
Enter 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).
aₙ = a₁r^(n−1), Sₙ = a₁(1−rⁿ)/(1−r)
How to use the Geometric Sequence Calculator
- 1Enter the first term.
- 2Enter the common ratio between terms.
- 3Enter the term number you need.
Worked example
Using the values the calculator loads with:
Inputs
- First term3
- Common ratio2
- Term number10
Results
- Term 101536
- Sum of first n terms3069
- Infinite sumDiverges
- Common ratio2
- First terms3, 6, 12, 24, 48, 96, 192, 384
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
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.