You have learnt now how to recognise linear sequences (such as 4, 7, 10, 13...) by the way they increase or decrease by the same amount each time.

If you look at the definition of a sequence though, 'a pattern of number that follows a rule', we have to look at the different types of sequence that follow different rules.

Fibonacci sequences: These sequences are generated by adding the previous two numbers in the sequence.

1, 1, 2, 3, 5, 8, 13, 21....

Square numbers: These are found by squaring the position of the number. So the first number is 1 x 1, the second is 2x2 etc

1, 4, 9, 16, 25, 36, 49...

Powers sequences: These are found by taking the power of a number. So the powers of 3, for example, would be 3^{1}, 3^{2}, 3^{3}, 3^{4}, 3^{5}...

3, 9, 27. 81. 243

These can be spotted quite easily as each one is a multiple of the previous one. (9 is 3 x 3, 27 is 9 x 3, 81 is 27 x 3)

Triangular Numbers. These are a bit harder to spot. Each time the difference increase by 1.

1, 3, 6, 10, 15

1 to 3 - Difference of 2

3 to 6 - Difference of 3

6 to 10 - Difference of 4

10 to 15 - Difference of 5

etc