What is an arithmetic sequence?

An arithmetic sequence is an ordered list of numbers in which consecutive terms differ by a constant value called the common difference (d). For example: 3, 7, 11, 15, ... has a common difference of 4.

What is the formula for the nth term?

The nth term is aₙ = a₁ + (n − 1) × d, where a₁ is the first term, n is the term position, and d is the common difference.

How is the sum of n terms calculated?

The sum of the first n terms is Sₙ = n / 2 × (2a₁ + (n − 1) × d), which is equivalent to Sₙ = n / 2 × (a₁ + aₙ).

Can the common difference be negative?

Yes. A negative common difference means the sequence is decreasing. For example: 20, 15, 10, 5, ... has d = −5.

Can I use decimal or fractional inputs?

Yes. All fields accept decimal values. For example, a first term of 0.5 and a common difference of 0.25 are both valid.

What is the difference between arithmetic and geometric sequences?

In an arithmetic sequence terms grow by addition (constant difference). In a geometric sequence terms grow by multiplication (constant ratio). This tool handles arithmetic sequences only.

Arithmetic Sequence Calculator

Name: Arithmetic Sequence Calculator
Availability: InStock
Author: Nham Vu

Find the nth term, partial sum, and common difference of any arithmetic sequence from two known values.

Sequence Parameters

First known value

Second known value

Term position n

Must be a positive integer.

Enter two values and press Calculate to see results.

Summary