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 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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