Geometric Sequence Term Calculator

About this calculator

A geometric sequence is a list of numbers where each term is found by multiplying the one before it by a fixed common ratio, r, such as 2, 6, 18, 54 (common ratio 3). The nth term is found directly with a_n = a₁ × r^(n−1), where a₁ is the first term — no need to multiply your way through every term in between.

Geometric sequences model any quantity that grows or shrinks by the same percentage or factor each step rather than by a fixed amount, which makes them the mathematical backbone of compound interest (each period's balance is the previous balance times (1 + rate)), population growth models, and radioactive decay, and they're taught in algebra right alongside arithmetic sequences to contrast additive versus multiplicative growth.

This calculator takes the first term, common ratio, and term position and returns the value of that specific term.