Geometric Sequence
A geometric sequence multiplies by a fixed common ratio r. This calculator finds the nth term aₙ = a₁·r^(n−1) and the partial sum Sₙ = a₁(1 − rⁿ)/(1 − r). When |r| < 1 it also reports the infinite sum S∞ = a₁/(1 − r).
Worked examples
Frequently asked questions
What is the nth term formula?
The nth term is aₙ = a₁·r^(n−1), where r is the common ratio.
When does the infinite sum exist?
The infinite geometric series converges only when |r| < 1, giving S∞ = a₁/(1 − r).
What if the ratio is 1?
Every term equals a₁, so the partial sum is simply a₁·n.