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Arithmetic Sequence Calculator

Find the nth term and the sum of an arithmetic sequence from the first term, common difference and n. See the formula and the first several terms listed out.

39
Term 10 (aₙ)
210
Sum of first 10 terms

Sequence & formulas

3, 7, 11, 15, 19, 23, 27, 31, 35, 39

aₙ = a₁ + (n − 1)d = 3 + (10 − 1) × 4 = 39

Sₙ = n⁄2 × (2a₁ + (n − 1)d) = 210

What is the Arithmetic Sequence Calculator?

The ByteTools Arithmetic Sequence Calculator works out any term and the running total of an arithmetic progression.

  • nth term and sum of the first n terms
  • Lists the opening terms of the sequence
  • Shows the arithmetic formulas used
  • Handles negative and decimal differences
  • Live results as you change the inputs
  • 100% private — runs entirely in your browser

How to use the Arithmetic Sequence Calculator

  1. 1

    Enter the first term of the sequence.

  2. 2

    Enter the common difference between consecutive terms.

  3. 3

    Enter n, the number of terms.

  4. 4

    Read the nth term, the sum of the first n terms and the listed terms.

  5. 5

    Click Copy to grab the results.

About the Arithmetic Sequence Calculator

The ByteTools Arithmetic Sequence Calculator works out any term and the running total of an arithmetic progression. Enter the first term, the common difference and how many terms you want, and it returns the nth term, the sum of the first n terms and a list of the opening terms.

It is built for algebra students, teachers and anyone modelling steady, linear growth such as savings plans or seat rows. The formulas for the nth term and the sum are shown so the method is clear, not just the answer.

All the maths runs in your browser with JavaScript. Nothing is uploaded, so it is private, instant and works offline. Copy the results with one click.

Frequently asked questions

What is an arithmetic sequence?

An arithmetic sequence is a list of numbers where each term differs from the previous one by a constant amount called the common difference. For example 3, 7, 11, 15 has a common difference of 4.

How do you find the nth term of an arithmetic sequence?

Use the formula aₙ = a₁ + (n − 1)d, where a₁ is the first term and d is the common difference. For 3, 7, 11 the 10th term is 3 + 9 × 4 = 39. The calculator applies this directly.

How do you find the sum of an arithmetic sequence?

The sum of the first n terms is Sₙ = n ÷ 2 × (2a₁ + (n − 1)d), or equivalently n times the average of the first and last term. The tool shows this figure alongside the nth term.

What is the common difference?

The common difference is the fixed amount added to each term to get the next one. Subtract any term from the one after it to find it. A positive difference makes the sequence rise; a negative one makes it fall.

Can the common difference be negative or a decimal?

Yes. A negative common difference produces a decreasing sequence, and a decimal difference produces fractional steps. The calculator accepts both and computes the terms and sum accordingly.

Guides for Arithmetic Sequence Calculator

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