How to Find the nth Term and Sum of a Sequence

To find the nth term and sum of an arithmetic sequence, enter the first term, the common difference and how many terms you want — the calculator applies aₙ = a₁ + (n − 1)d for the term and Sₙ = n⁄2 × (2a₁ + (n − 1)d) for the sum, and lists the opening terms so you can check the pattern. The ByteTools Arithmetic Sequence Calculator does all of this instantly and privately in your browser. Here is how to use it and what each field means.

What an arithmetic sequence is

An arithmetic sequence is a list of numbers where each term rises or falls by the same fixed amount, called the common difference. The sequence 5, 8, 11, 14 has a first term of 5 and a common difference of 3. Because the step is constant, you can jump straight to any term with a formula instead of adding your way there one step at a time — which is exactly what this tool automates.

Step-by-step: using the calculator

1. Enter the first term (a₁). This is where the sequence begins. It can be any number, including negatives and decimals.
2. Enter the common difference (d). This is the fixed amount added between consecutive terms. Use a negative value for a falling sequence and a decimal for fractional steps.
3. Enter n, the number of terms. This tells the tool how far along the sequence to go — both for the term it returns and for the sum.
4. Read the results. You get the nth term, the sum of the first n terms, and a list of the opening terms so you can eyeball the pattern.
5. Click Copy. Grab the results in one click to paste into homework, a spreadsheet or notes.

Because the results update as you type, you can experiment — change d and watch the sum swing — which makes it a genuine learning aid, not just an answer box.

A worked example

Suppose a₁ = 3, d = 4 and n = 10. The calculator computes:

Seeing the formula and the listed terms next to the answer means you can follow the method, not just copy the number — useful when you have to show your working.

Why in-browser and private matters

Every calculation runs locally in JavaScript. Nothing you type is uploaded, there is no sign-up, and once the page has loaded it works offline — handy during an exam-style practice session with no internet, or on a slow connection. For students and teachers, that means a fast, distraction-free tool that respects privacy and never gets in the way.

Try the Arithmetic Sequence Calculator — free and 100% in your browser.

FAQ

What do I enter if I only know two terms, not the difference?

Subtract the earlier term from the later one and divide by the number of steps between them to get the common difference, then enter that. For consecutive terms, the difference is simply the second minus the first.

Can I use it for a decreasing sequence?

Yes. Enter a negative common difference, for example −2, and the calculator produces a falling sequence and the correct nth term and sum.

What is the difference between the nth term and the sum?

The nth term is the single value at position n in the list. The sum is the total you get by adding the first n terms together. The calculator shows both at once so you do not have to compute them separately.

Does n have to be a whole number?

Yes — n counts terms, so it should be a positive whole number. The first term and common difference, however, can be negative or decimal values.

Related free tools

• Geometric Sequence Calculator — for sequences that multiply by a fixed ratio.
• Fibonacci Calculator — generate terms of the Fibonacci sequence.
• Average Calculator — quick means for any set of numbers.
• Percentage Change Calculator — measure growth or decline between values.

Built by ByteVancer

ByteTools is a free product of ByteVancer, a software and web development studio building web apps, SaaS and custom software. If you need reliable, well-built software for your own project, explore what ByteVancer can create for you.