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Number sequences are sets of numbers that follow a pattern or a rule.

If the rule is to add or subtract a number each time, it is called an arithmetic sequence.

If the rule is to multiply or divide by a number each time, it is called a geometric sequence.

Each number in a sequence is called a term.

A sequence which increases or decreases by the same amount each time is called a linear sequence.

Term to term rules

The term to term rule of a sequence describes how to get from one term to the next.

Example 1

Write down the term to term rule and then work out the next two terms in the following sequence.

3, 7, 11, 15, ...

Firstly, work out the difference in the terms.

This sequence is going up by four each time, so add 4 on to the last term to find the next term in the sequence.

3, 7, 11, 15, 19, 23, ...

To work out the term to term rule, give the starting number of the sequence and then describe the pattern of the numbers.

The first number is 3. The term to term rule is 'add 4'.

Once the first term and term to term rule are known, all the terms in the sequence can be found.

Example 2

Write down the term to term rule and then work out the next two terms in the following sequence.

-1, -0.5, 0, 0.5, ...

The first term is -1. The term to term rule is 'add 0.5'.