# Geometric Sequence Calculator

> Calculate the nth term (a_n), finite sum (S_n), or infinite sum (S) of a geometric sequence. Includes step-by-step derivation and convergence analysis.

**URL:** https://www.calculatoranswers.com/geometric-sequence-calculator
**Category:** Education

## Quick Answer

Calculate the nth term, finite sum, or infinite sum of a geometric sequence. Enter the first term, common ratio, and term count to view the results.

## Definition

A geometric sequence calculator computes progression terms, finite sums, and infinite sums of geometric series. It uses formulas such as a_n = a_1 * r^(n-1) and S_n = a_1 * (1-r^n)/(1-r), checking for convergence (when |r| < 1) to solve the infinite sum. It displays a step-by-step analysis and the first ten terms of the sequence.

## How to Use

1. **Enter sequence parameters** — Input the first term (a₁), the common ratio (r), and the number of terms (n).
2. **Choose target calculation** — Select whether to find the nth term, the sum of the first n terms, or the infinite sum.
3. **Read results** — View the results, convergence determination, step-by-step work, and a table of the first 10 terms.

## Disclaimer

This calculator provides estimates for educational and planning purposes. Always consult a qualified professional for specific advice on financial, medical, legal, or other regulated decisions.

---

*This page is part of Calculator Answers — simple calculators, clear answers, no signup required. View all calculators at https://www.calculatoranswers.com/calculators*