# Arithmetic Sequence Calculator

> nth term and sum of an arithmetic sequence from the first term and common difference.

Page: https://freecalculator.tech/tools/arithmetic-sequence-calculator
Last reviewed: 2026-11-03

## Formula

aₙ = a₁ + (n − 1)d; Sₙ = n(a₁ + aₙ) ÷ 2.

- Source: OpenStax College Algebra 2e §9.2 Arithmetic Sequences and §9.4 Series.
- aₙ = a₁ + (n − 1)d; Sₙ = n(a₁ + aₙ) ÷ 2.
- Inputs used: First term a₁, Common difference d, Term number n.

## Inputs

- First term a₁
- Common difference d
- Term number n

## Worked example: 3, 7, 11, … to the 10th term

a₁₀ = 39 and S₁₀ = 210.
1. a₁₀ = 3 + 9 × 4 = 39.
2. S₁₀ = 10 × (3 + 39) ÷ 2 = 210.

## Common questions

### Can the difference be negative?

Yes. A negative d makes the sequence decrease.

### How do I find d?

Subtract any term from the next one.

### Does n start at 1?

Yes. a₁ is the first term.

### How do I use the Arithmetic Sequence Calculator?

Enter the required values for First term a₁, Common difference d, Term number n. The calculator applies the formula on this page and shows the main result with any supporting breakdown so you can check the arithmetic.

### What formula does the Arithmetic Sequence Calculator use?

aₙ = a₁ + (n − 1)d; Sₙ = n(a₁ + aₙ) ÷ 2. The visible formula section above lists the calculation path and the edge cases the page handles, so the result can be checked without relying on the form alone.

### Can the Arithmetic Sequence Calculator be used for exact decisions?

Use it as a calculation aid, not as a substitute for checking the underlying rule, contract, policy, or professional advice that applies to your situation. When a result depends on local rules, personal details, prices, or dates, enter those values yourself and confirm them before acting.

## Limitations and assumptions

- Up to the 100,000th term.
- Floating-point rounding applies to decimals.
- Exact mathematical relationships, rounded for display. Check units and rounding before using a result in graded, engineering or financial work.
- The result depends on the values you enter for this arithmetic sequence calculator; it does not supply missing rates, rules, prices, dates, or assumptions for you.

## Sources

- OpenStax — https://openstax.org/books/college-algebra-2e/pages/9-2-arithmetic-sequences

## Cite this page

- APA: Free Calculator. (2026, November 3). Arithmetic Sequence Calculator. https://freecalculator.tech/tools/arithmetic-sequence-calculator
- MLA: "Arithmetic Sequence Calculator." Free Calculator, 3 Nov. 2026, https://freecalculator.tech/tools/arithmetic-sequence-calculator.
- Link: Arithmetic Sequence Calculator — Free Calculator, https://freecalculator.tech/tools/arithmetic-sequence-calculator