Math Tools

Number Sequence Generator

Generate arithmetic, geometric, Fibonacci, square, cube, prime and triangular number sequences instantly.

Advertisement
Number Sequence Generator
Arithmetic, geometric, Fibonacci, squares, cubes and more
Sequence

Disclaimer. This calculator is provided for educational and general-purpose use. Verify critical or high-stakes calculations independently before relying on them. Read full disclaimer →

About the Number Sequence Generator

This tool generates the first n terms of several classic number sequences. Arithmetic sequences add a constant difference d each step (a, a+d, a+2d, …). Geometric sequences multiply by a constant ratio r each step (a, a×r, a×r², …). The Fibonacci sequence starts at 1, 1 and each following term is the sum of the previous two. Perfect squares and perfect cubes are simply i² and i³ for i = 1, 2, 3, …. The primes option lists consecutive prime numbers using trial-division primality testing. Triangular numbers use the formula Tn = n(n+1)/2, representing the sum of the first n natural numbers.

The custom option takes your first two terms and continues the sequence by treating the difference between them as constant — effectively an arithmetic continuation rather than detecting a more complex underlying pattern (geometric, polynomial, etc.). For every sequence type, the tool also reports the sum of the generated terms and the value of the final term.

Frequently Asked Questions

Arithmetic (constant difference), geometric (constant ratio), Fibonacci (each term the sum of the previous two), perfect squares, perfect cubes, prime numbers, triangular numbers, and a custom mode that continues from your own first two terms.
Each term is a + i×d, where a is the first term, d is the common difference and i starts at 0. For example, with a=2, d=3 and 5 terms: 2, 5, 8, 11, 14 — and the tool also reports the sum, 40.
It takes the difference between your two entered terms and keeps adding that same difference to generate each following term. This means it continues an arithmetic pattern from your starting values rather than trying to detect a geometric, Fibonacci-style, or other more complex relationship — it's a simple linear continuation, not general pattern recognition.
Each triangular number is Tₙ = n(n+1)/2, which represents the sum of the first n natural numbers. So T₄ = 4×5/2 = 10, giving the sequence 1, 3, 6, 10, 15, ….
Advertisement