Sequence Calculator

What this tool does

Calculate sequence instantly in your browser. One field serves as the common difference (arithmetic) or the common ratio (geometric), depending on the selected type.

How to use the Sequence Calculator

1. Enter or select first term a₁.
2. Enter or select common difference d (arithmetic) or ratio r (geometric).
3. Enter or select term number n.
4. Enter or select sequence type.
5. Read the calculated result; change any measurement to compare alternatives.

Formula

Arithmetic: aₙ = a₁ + (n−1)d and Sₙ = n/2 × (2a₁ + (n−1)d). Geometric: aₙ = a₁ × r^(n−1) and Sₙ = a₁(rⁿ − 1)/(r − 1) for r ≠ 1.

a1

First term a₁

d

Common difference d (arithmetic) or ratio r (geometric)

termN

Term number n

type

Sequence type

One field serves as the common difference (arithmetic) or the common ratio (geometric), depending on the selected type.

Worked example

For sequence calculator, the following measurements illustrate the exact method: First term a₁: 3; Common difference d (arithmetic) or ratio r (geometric): 2; Term number n: 10; Sequence type: arith.

Results explained

Term n (aₙ)

Term n (aₙ) from the formula above. One field serves as the common difference (arithmetic) or the common ratio (geometric), depending on the selected type.

Sum of first n terms (Sₙ)

Sum of first n terms (Sₙ) from the formula above. One field serves as the common difference (arithmetic) or the common ratio (geometric), depending on the selected type.

First five terms

First five terms from the formula above. One field serves as the common difference (arithmetic) or the common ratio (geometric), depending on the selected type.

Frequently asked questions