Arithmetic Sequence Calculator

nth term and sum, with the off-by-one that catches everyone.

Written and maintained by Mohit PatelLast checked August 4, 2026How we build these

First term

Common difference

How many terms

Term 10

sum of the first 10 terms is 255

Term 1048

Sum255

First terms3, 8, 13, 18, 23, 28, 33, 38, 43, 48

Average term25.5

The nth term is a + (n−1)d — note the n−1, since the first term has had no difference applied yet. Off-by-one there is the commonest error in the topic. The sum is n/2 × (first + last), which is Gauss's trick: pair the first term with the last, the second with the second-last, and every pair has the same total. That is how he supposedly summed 1 to 100 in seconds — fifty pairs of 101. The average term always equals the average of the first and last, which is a quick way to check a sum by eye.

How the Arithmetic Sequence Calculator works

Enter a first term, a common difference and a term count for the nth term, the sum and the opening terms. The nth term uses n−1 differences rather than n, which is the single commonest slip in the topic.

Also known as: nth term calculator · arithmetic series sum calculator · common difference calculator · sum of an arithmetic sequence

Where to go next

The Arithmetic Sequence question rarely arrives on its own. These are the ones that usually come with it:

Geometric Sequence Calculator — nth term, sum, and whether the infinite series converges.
Average Calculator — Mean, median, mode, range, and standard deviation.
Percentage Calculator — Every common percentage question in one place.
Age Calculator — Exact age in years, months, days, and total units.

Sources

NIST Digital Library of Mathematical Functions

Frequently asked questions

What is the formula for the nth term?

a + (n−1)d. The n−1 matters: the first term has had no difference applied to it yet, so the tenth term has had nine added, not ten.

How do I sum an arithmetic series?

n/2 × (first + last), or equivalently n/2 × (2a + (n−1)d). Pair the first term with the last, the second with the second-last, and every pair has the same total.

How did Gauss sum 1 to 100 so quickly?

By pairing. 1+100, 2+99, 3+98 — fifty pairs each totalling 101, giving 5,050. That pairing is exactly what the sum formula encodes.

How do I find the common difference?

Subtract any term from the one after it. If the difference is not the same for every consecutive pair, the sequence is not arithmetic.

Put this calculator on your own site

Free to use, on any site, commercial or not. Paste this where you want it to appear. It is a plain iframe, so it works in WordPress, Squarespace, Wix, Webflow, Ghost and anything else that accepts HTML.

The one-line version

<iframe src="https://www.thecalclibrary.com/embed/arithmetic-sequence-calculator" width="100%" height="640" style="border:1px solid #e2e8f0;border-radius:12px" loading="lazy" title="Arithmetic Sequence Calculator"></iframe>
<p style="font:13px/1.5 system-ui,sans-serif;margin:6px 0 0;color:#64748b">Powered by <a href="https://www.thecalclibrary.com/arithmetic-sequence-calculator" style="color:#64748b">Arithmetic Sequence Calculator</a> from The Calc Library</p>

The only condition is that the credit line below the frame stays in place. That one line is what pays for the tool being free — it is how anyone else finds it.