Special sequences

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 \(n\)th term is \(n^2\)
cube numbers: 1, 8, 27, 64, 125, - the \(n\)th 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. The \(n\)th term is \(\frac{n(n+1)}{2}\)
Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, ... (in this sequence you start off with 1 and 1 and then to get each term you add the previous two terms), \(1 + 1 = 2\), \(1 + 2 = 3\), \(2 + 3 = 5\) and so on

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