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A sequence is a set of numbers arranged in a specific order.

A sequence has some key features:

• Each number in a sequence is called a term of the sequence
• Each term has a position, eg 1st, 2nd, 3rd etc
• The terms are linked by a pattern or rule
• The three dots at the end, ..., show that the sequence can keep going and more terms worked out

Here are some well-known number sequences that you should learn to recognise:

Even numbers

The terms are 2, 4, 6, 8...

Their positions are 1st, 2nd, 3rd, 4th...

To find the next term the rule is +2

Odd numbers

The terms are 1, 3, 5, 7...

The positions are 1st, 2nd, 3rd, 4th...

To find the next term the rule is +2

Square numbers

The terms are 1, 4, 9, 16...

The positions are 1st, 2nd, 3rd, 4th...

The rule is each term is formed by multiplying the position by itself:

Cube numbers

The terms are 1, 8, 27, 64...

The positions are 1st, 2nd, 3rd, 4th...

The rule is each term is formed by multiplying the position by itself three times:

Triangle numbers

The terms are 1, 3, 6, 10...

The positions are 1st, 2nd, 3rd, 4th...

The rule is that each term is previous term + position, eg:

4th term = 3rd term + 4

Powers of 2

The terms are 2, 4, 8, 16...

(2, 2 x 2, 2 x 2 x 2, 2 x 2 x 2 x 2...)

The positions are 1st, 2nd, 3rd, 4th...

To find the next term, the rule is x 2

Powers of 10

The terms are 10, 100, 1000, 10000...

(10, 10 x 10, 10 x 10 x 10, 10 x 10 x 10 x 10...)

The positions are 1st, 2nd, 3rd, 4th...

To find the next term, the rule is x 10