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Number Sequence Calculator

Choose the kind of sequence, enter the first term and the step, and say how many terms you want. You get the last term, the sum and the first terms of the sequence.

Your numbers

Result

How we calculate it

In an arithmetic sequence each term is the one before plus a common difference d, so the nth term is a + (n − 1) × d and the sum of the first n terms is n × (2a + (n − 1) × d) ÷ 2. In a geometric sequence each term is the one before times a common ratio r, so the nth term is a × r^(n − 1) and the sum is a × (r^n − 1) ÷ (r − 1), or n × a when r is 1. In a Fibonacci-style sequence each term is the sum of the two before it.

For example, starting at 2 and adding 3 gives 2, 5, 8, … with a 10th term of 29 and a sum of 155. Starting at 3 and doubling gives a 8th term of 384 and a sum of 765. The Fibonacci numbers 1, 1, 2, 3, 5, … reach 55 at term 10 and add up to 143.

Assumptions and limits

  • Up to 1000 terms are supported. The first 20 terms are listed in the table.
  • A geometric sequence has a sum to infinity only when the ratio is between −1 and 1. It is the first term divided by (1 − r).
  • For the Fibonacci option you choose the first two terms. Starting at 1 and 1 gives the classic sequence, and 0 and 1 gives the same numbers shifted by one place.

Frequently asked questions

How do I find the nth term of an arithmetic sequence?

Take the first term and add (n − 1) times the common difference. For 2, 5, 8, … the 10th term is 2 + 9 × 3 = 29.

What is the difference between arithmetic and geometric sequences?

An arithmetic sequence changes by adding the same amount each step, so it grows in a straight line. A geometric sequence changes by multiplying by the same factor each step, so it grows or shrinks by a constant percentage.

What is the Fibonacci sequence?

It starts with two terms and every later term is the sum of the previous two. With 1 and 1 it runs 1, 1, 2, 3, 5, 8, 13, 21, and so on.

Related calculators

Worked example (a fixed example using the starting numbers, it does not change as you type)

Inputs: Sequence type = Arithmetic (add the same number each time); First term = 2; Common difference = 3; Number of terms = 10.

  • nth term 29
  • Sum of the first n terms 155
  • Sequence 2, 5, 8, 11, 14, 17, 20, 23, 26, 29

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Last reviewed: . Formulas and assumptions are described on our methodology page. For information only; not professional advice.