You may already be familiar with recognising** linear sequences** (such as 4, 7, 10, 13, ...) which **increase or decrease by the same amount** each time.

However, if we look at the definition of a sequence, *(a pattern of numbers that follow the same rule)*, there are many other different types of sequences which follow different rules which it is helpful to be able to recognise too.

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

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

**Square numbers:** These sequences are created by squaring the position of the number. So the first number is 1 × 1, the second is 2 × 2, etc.

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

**Powers sequences: **These sequences are created using the power of a number. So the powers of 3, would be 3^{1}, 3^{2}, 3^{3}, 3^{4}, 3^{5}, ...:

e.g. 3, 9, 27, 81, 243, ...

These sequences can be spotted quite easily, as each number is a multiple of the previous one (i.e. 9 is 3 × 3; 27 is 9 × 3; 81 is 27 × 3; etc.)

**Triangular numbers: **These are a bit harder to spot, as each time the **difference** increases by 1.

e.g. 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.

In this activity, we will recognise and define the types of sequences shown, as well as finding unknown terms by continuing sequences in the same pattern.