Geometric Sequence Calculator
Compute the nth term and sum of a geometric sequence.
Input Data
A1
R
N
Results
The nth term.
1,024
Sum of the first n terms.
2,046
Explanatory note about the result.
a_10=1024；S_10=2046
At a glance:a_n = a1·r^(n−1); S_n = a1·(1−rⁿ)/(1−r) for r≠1. Complements geometric-sequence and sequence.
Formula
a_n = a1·r^(n−1).
S_n = a1(1−rⁿ)/(1−r).
How to Use
- Enter a1, r and n.
- The tool returns the nth term and sum.
Case Studies
a1=2, r=3, n=4
a4 = 2·27 = 54; S4 = 2(1−81)/(1−3) = 80.
FAQ
What if r=1?
Then every term equals a1 and S_n = n·a1.
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References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.