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

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

An arithmetic sequence is a list of numbers where each term increases (or decreases) by a fixed amount called the common difference. This calculator lets you enter any two known values — such as the first term and common difference, or two specific terms — and instantly computes the full picture: the nth term, the partial sum up to n terms, and the common difference. Results update in real time as you type.

How it works

Select which two values you already know from the dropdown menus.
Enter those two values in the input fields.
Set the term position n you want to evaluate.
The calculator solves for the nth term (aₙ), the sum of the first n terms (Sₙ), and the common difference (d).
Use the sequence preview to verify the first several terms look correct.

Use cases

Check homework answers for arithmetic sequence problems.
Find how many terms are needed to reach a target sum.
Model linear growth scenarios such as salary raises or savings plans.
Verify that a data series is arithmetic by computing a consistent common difference.
Generate the first N terms of a sequence for pattern analysis.
Solve for a missing first term when only later terms are known.

Frequently Asked Questions

Last updated: 2026-05-30 · Reviewed by Nham Vu