Extend an arithmetic, geometric or Fibonacci sequence

Homework sequences and pattern puzzles: pick the rule, get the next hundred terms — or ten thousand — with the Nth term on demand.

Tools used in this guide

The job

Given a first term and a step, arithmetic sequences add it each time, geometric multiply, and Fibonacci adds the previous two terms. Listing them by hand is fine for ten terms — not for the 500th.

Rule in, terms out

Pick arithmetic (a, a+d, a+2d…), geometric (a, ar, ar²…) or Fibonacci. Enter the first term(s), the step or ratio, and how many terms — up to 10,000. The Nth term is computed directly, no scrolling needed.

Fibonacci seeds the first two terms separately — the classical 1,1 is just the default.
Fibonacci output caps at 5,000 digits per term; the 10,000th Fibonacci number is about 2,090 digits, so it's fine.

Reality checks

Geometric sequences explode fast — ratio 2 for 10,000 terms is an astronomical number, and the output is formatted, not approximated silently. If terms look wrong, check the direction of the ratio (0.5 shrinks, 2 grows).