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Number Sequence Calculator

Arithmetic, geometric and Fibonacci terms and sums.

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The sequence

—

Term by term

nTermRunning sum

The nth term

—

Sums

Sum of first n terms—
Infinite sum—
Sum of listed terms—

Properties

Type—
Behaviour—

An arithmetic sequence adds a fixed amount each time; a geometric one multiplies by a fixed ratio; a Fibonacci sequence adds the two previous terms. An infinite geometric series only has a finite sum when the common ratio lies strictly between −1 and 1.

Quick Tool Overview

The Number Sequence Calculator handles the three sequences that cover almost all coursework — arithmetic, geometric and Fibonacci. It finds any term, lists the sequence out and totals it, printing the formula with your own values substituted in.

What it does
Finds terms and sums of arithmetic, geometric and Fibonacci sequences
You give it
A first term, a difference or ratio, and how many terms
You get back
The nth term, the listed sequence and its sums
Best for
Homework, exam revision and checking your own working
Calculators Free, unlimited use No sign-up Runs in your browser

About the Number Sequence Calculator

Work with the three sequences that cover almost all coursework: arithmetic, where each term adds a fixed amount; geometric, where each term multiplies by a fixed ratio; and Fibonacci, where each term is the sum of the two before it.

For any of them you can find the nth term, list the sequence out, and total it — including the infinite sum of a geometric series, which converges only when the common ratio sits strictly between minus one and one. The formula used is printed alongside every result with your own numbers substituted in, because in a sequences question the working is usually what is being marked rather than the final figure.

Key features of the Number Sequence Calculator

Three sequence types

Arithmetic, geometric and Fibonacci, each with its own parameters rather than a single generic form.

The formula, substituted

Every result shows the formula with your numbers in it, because the working is usually what gets marked.

Infinite geometric sums

Calculated where the series converges, and explicitly refused where the ratio makes it diverge.

The sequence listed out

Terms are printed so you can sanity-check the pattern rather than trusting one number.

Partial sums included

The total of the first n terms alongside the nth term itself.

How to use the Number Sequence Calculator

  1. 1

    Choose the sequence type

    Arithmetic, geometric or Fibonacci.

  2. 2

    Enter the parameters

    A first term plus a common difference or ratio, and how many terms you want.

  3. 3

    Read the nth term

    Any term you ask for, with the formula shown using your values.

  4. 4

    Check the sums

    The partial sum of the terms listed, and the infinite sum where a geometric series converges.

Frequently asked questions

The nth term is a + (n − 1)d, where a is the first term and d is the common difference. The sum of n terms is n/2 × (2a + (n − 1)d).

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