Geometric Sequence Calculator - Calculator See


Geometric Sequence Calculator

Calculate the nth term, common ratio (r), and sum of finite or infinite geometric sequences.

Calculator Inputs

Starting term.
Multiplier between terms.
Which term to find.

Calculated Results

N-th Term Value (a_n)
768 (at n = 9)
Sum of First n Terms (S_n) 1,533
Common Ratio (r) 2.000
Infinite Sum S_inf Diverges (|r| >= 1)
Values calculate live as you adjust inputs.

About Geometric Sequence Calculator

Analyzes geometric progressions where each successive term is generated by multiplying the preceding term by a constant ratio r.

What is Geometric Sequence Calculator?

Analyzes geometric progressions where each successive term is generated by multiplying the preceding term by a constant ratio r.

How to Use This Calculator

  1. Enter initial term a1 and common ratio r.
  2. Enter term position n.
  3. View nth term value and series sum Sn.

The Mathematical Formula & Variables

an = a1 * r^(n-1); Sn = a1 * (1 - r^n) / (1 - r)

Step-by-Step Worked Example

Scenario: a1 = 3, r = 2, find 9th term.

  1. a9 = 3 * 2^(9-1) = 3 * 2^8 = 3 * 256 = 768.
  2. Sum S9 = 3 * (1 - 512) / (1 - 2) = 3 * 511 = 1533.

Result: 768

Frequently Asked Questions

When does an infinite geometric series converge?

An infinite geometric series converges to S = a1 / (1 - r) if and only if the absolute value of the common ratio is strictly less than 1 (|r| < 1).