Number sequences

A pattern or a sequence is a set of numbers that are connected in some way. All sequences have a rule.

For example, sometimes the numbers might count on by 5 each time, other times they might be doubled.

Some sequences are easier to spot than others. If you can spot the rule, you can work out the pattern.

The numbers in the sequence are called terms.

Complete this interactive activity to understand how to use number sequences. Then put your knowledge to the test.

A number sequence is a set of numbers connected in some way.

Number sequences can contain numbers that increase or decrease by a step or set amount each time.

Take a look at this number sequence.

Look at the difference between the terms in the sequence. Can you see the difference between each term is 6?

12 - 6 = 6

18 - 12 = 6

24 - 18 = 6

Therefore, the rule is +6.

If the pattern continues the next term will be:

30 + 6 = 36

The next number is 36.

However, number sequences don’t always increase by the same amount each time.

Let’s look at another one.

If you can work out the rule that the sequence is using, you can continue the sequence or even find missing numbers.

The first step is to look at the difference between each pair of numbers in the sequence.

The difference between each pair of terms is a different amount each time.

3 – 1 = 2

6 - 3 = 3

10 – 6 = 4

15 – 10 = 5

If the pattern continues, then the next difference will be +6, meaning that the next term is 21 (15 + 6).

Example 2

Example 3