Geometric Sequence Generator

What this generator does

Produces a geometric sequence: each term is the previous one multiplied by a fixed ratio. Contrasts with an arithmetic sequence, where a fixed amount is added instead.

How to use this tool

1. Press generate for a random geometric sequence.

Worked examples

Example shape

3, 6, 12, 24, 48 — ratio 2

Common use cases

• Maths practice spotting geometric patterns
• Teaching the difference between arithmetic and geometric sequences
• Quick number-pattern puzzles

How this generator works

A first term and a ratio are drawn, and each term is the previous one multiplied by that ratio. Building by repeated multiplication rather than by raising the ratio to a power keeps the terms exact for as long as the arithmetic allows, and makes the defining property visible: every consecutive pair has the same ratio.

Limitations and good to know

• A ratio above one makes terms grow very quickly, so a long sequence can reach numbers too large to be useful.
• Terms grow or shrink exponentially, so a modest ratio over a dozen terms produces numbers no longer suitable for mental arithmetic.
• The ratio is never zero or one — either makes the sequence constant or collapses it, and neither is a useful exercise.
• A negative ratio alternates the sign of the terms, which is correct and often surprising.