Special sequences

There are some special sequences that you should be able to recognise are not linear or quadratic.

The most important of these are:

square numbers: 1, 4, 9, 16, 25, 36, … - the \(n\)th term is \(n^2\)
cube numbers: 1, 8, 27, 64, 125, - the \(n\)th term is \(n^3\)
triangle 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, ... (starting with 1, 1, add the last two terms together to get the next term)
Fibonacci-type sequences, eg: 1, 3, 4, 7, 11, 18,... (follow the same rule as the Fibonacci sequence but use other starting terms)

Sequences - OCRSpecial sequences