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Arithmetic sequence calculator

Find the nth term and the sum of an arithmetic sequence.

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Enter First term (a), Common difference (d), Number of terms (n) and the Arithmetic sequence calculator works out nth term, Sum of terms straight away. For instance, with First term (a) = 2, Common difference (d) = 3 and Number of terms (n) = 10 it returns nth term = 29 and Sum of terms = 155.

How to use it

  1. Enter your values: First term (a), Common difference (d), Number of terms (n).
  2. Read the result instantly: nth term, Sum of terms.

Frequently asked questions

What does the Arithmetic sequence calculator actually compute?

It takes First term (a), Common difference (d) and Number of terms (n) and derives nth term and Sum of terms from them. The calculation is live as you type, so the result updates on every change.

What information do I need to provide?

3 values: First term (a), Common difference (d) and Number of terms (n). Nothing else is required — no account, no file upload.

Can you show a worked example?

With First term (a) = 2, Common difference (d) = 3 and Number of terms (n) = 10, the calculator returns nth term = 29 and Sum of terms = 155. Those figures come from running this exact tool, so you can reproduce them by entering the same values.

What happens if I enter larger values?

It moves a lot. Using First term (a) = 4, Common difference (d) = 6 and Number of terms (n) = 20 instead, nth term goes from 29 to 118 — which is why it is worth testing a few scenarios rather than trusting a single figure.

What does it give for smaller values?

Scaled down to First term (a) = 1, Common difference (d) = 2 and Number of terms (n) = 5, nth term comes out at 9. The relationship is worth checking at both ends before you rely on a single result.

When would I actually use this?

Finding the nth term without listing every one before it, summing a long run in one step, and recognising which family a sequence belongs to.

What is the most common mistake?

Starting the index at the wrong end. Whether the first term is a₀ or a₁ shifts every result by one position, and the two conventions are both common.

What is the difference between the Arithmetic sequence calculator and the Geometric sequence calculator?

Both return nth term and Sum of terms. What differs is what they ask for: this one wants Common difference (d), the Geometric sequence calculator wants Common ratio (r). Use whichever matches the numbers you already have.

Is there a tool for the next step?

Graphical degree sequence validator is the closest one after this: Can a list of vertex degrees actually be realised by a simple graph? Enter the degrees and the Erdős–Gallai / Havel–Hakimi test decides whether the sequence is graphical — a real network with those connection counts exists — and explains the verdict.

What else is worth having open alongside it?

List of Fibonacci numbers and Cube numbers list — they come up in the same task often enough to be worth a second tab.

Further reading

All guides →
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