Calculate a term and the sum of the first n terms

Students and teachers use it to verify a requested term or the sum of the first n terms in an arithmetic sequence.

Calculate a term and the sum of the first n terms. Everything runs in your browser, so the values you enter are never uploaded, shared, or stored.

How to use

Enter the first term of the sequence on the first line of the field.
Set the common difference, the value added at each step.
Give the rank n you want, counting from one.
Run calculate to get that term and the sum of the first n terms.
Compare the answer with your lesson or exercise to check the formula.

Example

For a sequence that starts at three with a common difference of five, ask for the tenth rank. The tool returns the matching term and the sum of the first ten terms. This makes it easy to check homework before writing out the proof. Watch the sign if the difference is negative.

Input

3
5
10

Limits and formats

It handles arithmetic sequences, not geometric ones.
The common difference may be negative, but the rank n must be a positive whole number.
The output does not show the full formula step by step.
Check the context if the sequence models a real-world situation.
A very high rank can produce a number that is hard to interpret, so keep examples realistic.

Where processing happens

The calculation runs locally in your browser. The first term, common difference and rank stay on your device and are not sent away. The results appear directly on the page and can be written down for later use.

Frequently asked questions

What is the common difference in an arithmetic sequence?

It is the fixed value added to move from one term to the next. A positive difference makes the sequence grow, a negative one makes it fall, and a difference of zero keeps every term equal. It is the key value in the formula.

Can I ask for a very high rank?

Yes, as long as the number is a positive whole number. A very large rank may be less practical to read, but the calculation follows the same rule. Use a value that fits your exercise and check the result.

Does the sum start at the first term?

Yes, the sum covers the first n terms, from rank one up to the rank you requested. If you need a partial sum between two ranks, subtract one total from the other or run separate calculations. The tool does not show the intermediate steps.