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Calculation Machine

Arithmetic Sequence Calculator

nth term and sum of an arithmetic series.

Reviewed by the Calculation Machine team · How we check our maths

Your values

ⓘ Live results

Results
Term 20
98
Sum of first n terms
1010
Common difference
5
First terms
3, 8, 13, 18, 23, 28, 33, 38, 43, 48

Quick answer

In an arithmetic sequence each term adds a fixed common difference, so the nth term is a₁ + (n−1)d.

The formula

aₙ = a₁ + (n−1)d, Sₙ = n/2 (a₁ + aₙ)

Worked example

Worked example

Using the values the calculator loads with.

Inputs

  • First term3
  • Common difference5
  • Term number20

Result

  • Term 2098
  • Sum of first n terms1010
  • Common difference5
  • First terms3, 8, 13, 18, 23, 28, 33, 38, 43, 48

How to use the Arithmetic Sequence Calculator

  1. 1Enter the first term of the sequence.
  2. 2Enter the common difference between terms.
  3. 3Enter which term number you want.

Frequently asked questions

What if the difference is negative?

The sequence decreases; the formulas still work exactly the same.

How is this different from geometric?

Arithmetic adds a constant, geometric multiplies by a constant.

About this calculator