Geometric Sequence Calculator
Term n, the sum of the first n terms and the infinite sum of a geometric progression.
Results
Term at position n
4374.000000
Sum of the first n terms
6560.000000
Total
0.000000
What this tool does
A geometric sequence multiplies by the same factor at every step, which is the shape of compound interest, population growth and radioactive decay. When the ratio is between −1 and 1 the terms shrink and the infinite sum converges, which is the third result.
Formula
aₙ = a₁ × rⁿ⁻¹ , Sₙ = a₁ × (rⁿ − 1) ÷ (r − 1)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
a | First term | — |
r | Common ratio | — |
n | Position n | — |
AN | Term at position n | — |
SN | Sum of the first n terms | — |
SI | Total | — |
Worked example
- First term2
- Common ratio3
- Position n8
- Term at position n4374.000000
- Sum of the first n terms6560.000000
- Total0.000000
Limitations
- The calculation runs at full precision and only the display is rounded. If you copy an intermediate value and retype it, small differences can appear.