Formula and method
aₙ = a₁r^(n − 1). For r ≠ 1, Sₙ = a₁(1 − rⁿ)/(1 − r). For r = 1, Sₙ = na₁.
Worked example
Starting at 2 with ratio 2, the tenth term is 1,024 and the first ten terms sum to 2,046.
Geometric Sequence Calculator
Find a geometric sequence’s nth term and finite sum from its starting term, common ratio and term count.
Printed from Calxy · https://www.calxy.net/math/geometric-sequence-calculator
Term 101,024.0000
-1000000000 – 1000000000
-1000000000 – 1000000000
terms
1 – 10000
Term 10
1,024.0000
- Sum of first 10 terms2,046.0000
| Index | Term |
|---|---|
| 1 | 2 |
| 2 | 4 |
| 3 | 8 |
| 4 | 16 |
| 5 | 32 |
| 6 | 64 |
| 7 | 128 |
| 8 | 256 |
| 9 | 512 |
| 10 | 1024 |
Term indices start at 1. Very large geometric powers can exceed floating-point range; reduce the term count or ratio if the calculator reports an overflow.
How this was calculated
aₙ = a₁r^(n − 1).
Sₙ = a₁(1 − rⁿ)/(1 − r), or n × a₁ when r = 1.
Frequently asked questions
What happens when the ratio is one?
Every term equals the first term, so the sum is the first term multiplied by the count. The calculator handles this without dividing by zero.
Last updated . Results are estimates for informational purposes only.