Special sequences

Explore updated revision resources for GCSE Maths: Special sequences, with step-by-step slideshows, quizzes, practice exam questions, and more!

There are some special sequences that you should be able to recognise.

The most important of these are:

Square numbers: 1, 4, 9, 16, 25, 36, … - the nth term is \(n^2\).
Cube numbers: 1, 8, 27, 64, 125, ... - the nth term is \(n^3\).
Triangular numbers: 1, 3, 6, 10, 15, ... (these numbers can be represented as a triangle of dots). The term to term rule for the triangle numbers is to add one more each time: \(1 + 2 = 3\), \(3 + 3 = 6\), \(6 + 4 = 10\) etc.
Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, ... (in this sequence you start off with 1 and then to get each term you add the two terms that come before it).

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