How to use the Sequence Calculator
- Choose arithmetic (add the same amount) or geometric (multiply by the same amount).
- Enter the first term and the common difference or ratio.
- Enter n to see the nth term, the sum and the list of terms.
What does this tool do?
In an arithmetic sequence each term adds a fixed difference d: 3, 7, 11, 15… In a geometric sequence each term multiplies by a fixed ratio r: 3, 6, 12, 24…
Sequences model regular savings, depreciation, population growth and many textbook problems. The calculator lists up to the first 100 terms so you can check the pattern.
Why use it?
- Both sequence types.
- nth term and partial sum together.
- Lists the terms for checking.
The formula
Arithmetic: aₙ = a₁ + (n − 1)d, Sₙ = n(2a₁ + (n − 1)d) ÷ 2
Geometric: aₙ = a₁ rⁿ⁻¹, Sₙ = a₁(1 − rⁿ) ÷ (1 − r)
Privacy
The calculation happens instantly in your browser. The numbers you enter are not sent to our servers or saved. There's no account to create and nothing to install.
Frequently asked questions
What's the difference between a sequence and a series?
A sequence is the list of terms; a series is what you get when you add them up. Use the Series Calculator for sums of any expression.
Last reviewed by the M2Toolkit team.