Number Sequence Calculator

Choose arithmetic or geometric, enter the first term and the common difference or ratio, then the term number n.

How it works

An arithmetic sequence adds a constant d: aₙ = a₁ + (n−1)d, and the sum is n/2 times (first + last).

A geometric sequence multiplies by a constant r: aₙ = a₁ rⁿ⁻¹. If r = 1 the geometric sum is just n a₁; otherwise Sₙ = a₁(rⁿ − 1)/(r − 1). n must be a positive integer. Overflow is rejected instead of Infinity.

Formula

Arithmetic: aₙ = a + (n − 1)d,  Sₙ = n/2 × (2a + (n − 1)d)
Geometric: aₙ = a rⁿ⁻¹,  Sₙ = a(rⁿ − 1)/(r − 1)  (r ≠ 1)

Worked examples

Arithmetic 2, 5, 8, …
a = 2, d = 3, n = 5 → a₅ = 14, S₅ = 40
Geometric 3, 6, 12, …
a = 3, r = 2, n = 4 → a₄ = 24

Useful notes

This is not a list-of-numbers summary. Paste a finished list into the statistics calculator.

FAQ

How do I find the nth term of an arithmetic sequence?: Add the common difference (n − 1) times: aₙ = a₁ + (n − 1)d.
How do I find the nth term of a geometric sequence?: Multiply the first term by r to the power n − 1.
What if the ratio is 1?: Every term equals the first term. The sum of n terms is n × a₁.

Related tools

See all Statistics tools.