Geometric Sequence Calculator
aₙ = a₁ × r^(n−1). Find any term of a geometric sequence.
Result
How to use this calculator
- Enter a₁, ratio r, and n.
About this calculator
Geometric sequence: each term is the previous × constant ratio r. Formula aₙ = a₁ × r^(n−1). Sum: Sₙ = a₁(1 − rⁿ)/(1 − r) for r ≠ 1. Examples: doubling (r=2), halving (r=½), compound interest (r = 1+rate), bouncing-ball heights (r<1), nuclear chain reactions. Infinite sum converges if |r| < 1: S∞ = a₁/(1−r).
Frequently asked
r = 1 case?+
Negative r?+
|r| < 1 infinite sum?+
Compound interest?+
Difference from arithmetic?+
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