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Math

Geometric Sequence Calculator

Generate terms and a finite sum for a sequence with a constant multiplier.

Exact method explained belowEditable inputs

Set up your calculation

Runs on your device

SOLUTION

Your result

Let’s calculate.

Use the Calculate button to see your result.

Review the method below for assumptions and conventions.

How to use this tool

  1. Enter first term, common ratio, number of terms.
  2. Select Calculate to view the result.
  3. Check the method and assumptions below before using the result.

The method, explained

Term n = first term × ratio raised to (n − 1). The tool multiplies successively and adds the requested terms, including the ratio = 1 case without division by zero.

A WORKED EXAMPLE

For first term 2 and ratio 3, five terms are 2, 6, 18, 54, 162. Their sum is 242.

What to keep in mind

Calculates a finite sequence, not an infinite sum. Up to 1,000 terms; only the first 20 are listed. Values beyond 10^100 are rejected, and extremely small values may underflow in browser arithmetic.

Common questions

What does a negative ratio do?

For a nonzero first term, signs alternate. For example, ratio −2 produces 1, −2, 4, −8.

What happens with a zero ratio?

The first term stays as entered; every later term is zero.

Methodology maintained by ClarityKit. How these tools are built and checked.