Multiplicative sequence terms and sums
Geometric Sequence Calculator
Calculate a geometric sequence’s nth term, finite sum, first terms, explicit formula, recursive formula, and convergence behavior.
Use finite decimal values and a positive whole-number term from 1 through 100,000. The preview is capped at 12 terms.
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Geometric sequence result
First terms:
Nth term:
Finite sum:
Explicit formula:
Recursive formula:
Infinite series:
Method, ownership, and limits
The calculator uses aₙ = a₁r^(n−1). For r ≠ 1, it uses Sₙ = a₁(1−rⁿ)/(1−r); for r = 1, it uses Sₙ = na₁. The infinite series converges only when |r| < 1. Every result is checked for JavaScript numeric overflow before display.
This page owns multiplicative-ratio sequences. Arithmetic Sequence Calculator retains additive-difference sequences.
Inputs and results stay in this browser tab. They are not placed in URLs, saved in browser storage, or sent to a remote calculation service.