Arithmetic Sequence Calculator

Find an arithmetic sequence’s nth term, finite sum and first terms from the initial value and common difference.

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Term 1029.0000

First term (a₁)

The number the sequence starts with.

Common difference (d)

The amount added to get from one term to the next. Use a negative number to count down.

Number of terms / term index

terms

Which term to find (n). The sum adds up the first n terms.

Term 10

29.0000

Sum of first 10 terms155.0000

First terms (up to 30)
Index	Term
1	2
2	5
3	8
4	11
5	14
6	17
7	20
8	23
9	26
10	29

Term indices start at 1. Very large geometric powers can exceed floating-point range; reduce the term count or ratio if the calculator reports an overflow.

How this was calculated

Start at 2 and add the common difference (the amount added each time), 3, to get each next term.2, 5, 8, 11, …
To jump straight to term 10, add the difference 9 times (one fewer than n, because the first term is already there).aₙ = a₁ + (n − 1)d.Put in your numbers: a₁₀ = 2 + (10 − 1) × 3Answer: 29
To add up the first 10 terms, take the average of the first and last terms and multiply by how many terms there are.Sₙ = n(a₁ + aₙ)/2.Put in your numbers: S₁₀ = 10 × (2 + 29) ÷ 2Answer: 155

Arithmetic sequences in simple words

An arithmetic sequence is a list of numbers where you add the same amount each time. That amount is called the common difference.

For example, start at 2 and keep adding 3: 2, 5, 8, 11, 14 and so on. The common difference is 3.

To find a far-away term without writing them all, add the difference one fewer time than the term number. The 10th term is 2 + 9 × 3 = 29.

To add up the first 10 terms, pair the first and last terms: (2 + 29) ÷ 2 = 15.5 is their average, and 10 × 15.5 = 155.

Formula and method

aₙ = a₁ + (n − 1)d. The sum is Sₙ = n(a₁ + aₙ)/2, with term numbering starting at one.

Worked example

Starting at 2 with difference 3, the tenth term is 29 and the first ten terms sum to 155.

Frequently asked questions

Can the difference be negative?

Yes. A negative difference creates a decreasing sequence. Term counts must remain positive whole numbers.

Last updated September 27, 2026. Results are estimates for informational purposes only.