Ten Sequence Types in One Generator
This number sequence generator covers ten distinct sequence types in one place: arithmetic sequence generator online mode for evenly-spaced progressions, geometric sequence generator mode for constant-ratio progressions, plus Fibonacci, prime, square number sequence generator, cube number sequence generator, triangular number generator, power sequence generator, factorial sequence generator, and a custom number sequence formula mode for anything the built-in types don't cover. If you specifically need deep Fibonacci features like finding the nth term by index or checking whether a given number belongs to the sequence, or prime-specific tools like factorization and primality testing, the dedicated Fibonacci Calculator and Prime Number Checker on this site go further in those two areas alone. This generator's strength is breadth, ten sequence types with one consistent interface, rather than depth on any single one.
How to Use This Number Sequence Generator
Pick a sequence type from the toolbar, arithmetic, geometric, Fibonacci, primes, squares, cubes, triangular, powers, factorial, or custom formula. Depending on the type, fill in the relevant fields: Start and Step for arithmetic, Start and Ratio for geometric, Start and Exponent for a power sequence, or a formula expression for custom mode. Set Count to control how many terms to generate (1 to 100) and Separator to control how terms are joined (comma space, newline, or plain space) in the output. Results update automatically as you change any field, no Generate button needed, then copy or download the sequence as a text file.
Writing a Custom Sequence Formula
Custom formula mode lets you define your own a(n) expression using n as the term index, starting at 1 for the first term. Basic arithmetic operators (+, -, *, /), parentheses, and ^ for exponentiation are supported, evaluated safely in a sandboxed context that only permits numeric expressions, not arbitrary code. This is useful for sequences the built-in types don't cover directly, like every other even number, a shifted quadratic, or a formula specific to a problem you're working through.
| Formula | Produces (first 5 terms) | Description |
|---|---|---|
| n * 2 | 2, 4, 6, 8, 10 | Even numbers |
| n * n + 1 | 2, 5, 10, 17, 26 | Squares plus one |
| 2 ^ n | 2, 4, 8, 16, 32 | Powers of two, equivalent to a geometric sequence with ratio 2 |
Arithmetic vs. Geometric: What's the Difference
An arithmetic sequence adds the same fixed amount (the step) to get from one term to the next, so the difference between consecutive terms is always constant. A geometric sequence instead multiplies by a fixed ratio to get the next term, so it's the quotient between consecutive terms that stays constant, not the difference. This is why geometric sequences with a ratio greater than 1 grow much faster than arithmetic ones with a comparable step, the growth compounds multiplicatively rather than accumulating additively.
| Type | Rule | Example (start 1) |
|---|---|---|
| Arithmetic | a(n) = start + (n minus 1) times step | 1, 3, 5, 7, 9 (step 2) |
| Geometric | a(n) = start times ratio^(n minus 1) | 1, 3, 9, 27, 81 (ratio 3) |