Geometric Sequence Calculator
nth term and sum of a geometric series.
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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
- 1Enter the first term.
- 2Enter the common ratio between terms.
- 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.