Number Sequence Calculator

Sequence Type

How many terms (n)

Caps: arithmetic/triangular/square 5,000; geometric 3,000; Fibonacci 2,000; primes 5,000.

First term (a₁)

Difference (d)

Ratio (r)

F₁ (first)

F₂ (second)

Number Sequence – Quick Cheat Sheet

Arithmetic: aₙ = a₁ + (n−1)·d; sum Sₙ = n(a₁ + aₙ)/2.
Geometric: aₙ = a₁·rⁿ⁻¹; sum Sₙ = a₁(1−rⁿ)/(1−r) (if r ≠ 1), else Sₙ = n·a₁.
Fibonacci-like: aₙ = aₙ₋₁ + aₙ₋₂ (n≥3) with custom F₁, F₂.
Triangular: Tₙ = n(n+1)/2; 1, 3, 6, 10, …
Squares: aₙ = n²; 1, 4, 9, 16, …
Primes: first n primes via Sieve of Eratosthenes.
Caps prevent overload; very large n can be heavy (geometric and Fibonacci grow quickly).