Number Pattern Generator & Solver

Generate custom algebraic sequences or analyze a list of numbers to automatically solve and predict the pattern.

Pattern Type

a_n = a + (n-1)·b — each term increases by a fixed step (a = start, b = step)

Start (a)

Step (b)

Count

Format

Sequence Stats

Terms

Min

Max

Sum

225

Convergence:

Divergent (step ≠ 0)

Sequence Output

1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29

Visualization

About the Number Pattern Generator & Solver

Mathematical sequences are fundamental to number theory, computer science, and nature. Arithmetic sequences increase by a constant amount each step; geometric sequences multiply by a constant ratio. The Fibonacci sequence (1, 1, 2, 3, 5, 8…) appears throughout nature in spirals and growth patterns.

This solver parses lists of numbers to identify linear (arithmetic), exponential (geometric), Fibonacci-like, or quadratic sequences, producing mathematical formulas and predicting subsequent terms.

Built and maintained by Meet Shah · Last updated 14 August 2026

What this tool is used for

Producing a named sequence for a lesson or a puzzle.
Generating terms to check an implementation against.
Comparing growth rates across sequence types.
Producing a fixture of known values to test a sequence implementation.
Exploring a sequence's behaviour over many terms.

Frequently Asked Questions

Which sequences are built in?: Eleven: arithmetic, geometric, Fibonacci, Lucas, primes, triangular, square, cube, powers, factorial and a custom formula. Lucas is worth singling out — same recurrence as Fibonacci but seeded 2, 1 instead of 1, 1, and its ratio of consecutive terms converges to the same golden ratio.
What can I write in a custom formula?: An expression in n using + − × ÷, ^ for powers, and the whitelisted names sin, cos, tan, sqrt, pow, abs, pi and e. `2*n+5`, `n^2-n` and `pi*n` all work. Anything else — a variable name, a function that is not on the list — evaluates to NaN by design rather than reaching the JavaScript engine.
Is the custom formula safe to use with an expression from someone else?: It is guarded on two levels: a character filter rejects brackets, quotes, commas and backticks outright, and every remaining identifier is either substituted with its Math equivalent or replaced by NaN. Nothing survives that can reach a global, and the result is discarded unless it is a finite number.
Why does the term count stop at 100?: Because several of these outgrow any display: 100! is a 158-digit number, and 2^100 has already left exact integer range. Capping the count keeps the output readable and stops a factorial or power sequence from producing a column of Infinity — the shape stays visible without pretending it is exact.
How does triangular differ from square?: T_n = n(n+1)/2 counts dots in a triangle — 1, 3, 6, 10, 15 — and each term adds the next integer. S_n = n² adds the next ODD number instead: 1, 4, 9, 16. The two are related: any square number is the sum of two consecutive triangular numbers, which is 9 = 3 + 6.

Common errors and gotchas

Disagreeing on the starting index, where conventions differ per sequence.
Overflowing on a fast-growing sequence, where terms exceed the number range quickly.
Assuming a sequence's name is unambiguous, since several have competing definitions.
Treating a finite sample as proof of the general rule.
Confusing triangular, square and cube numbers, which grow at different rates.