Sequences

Trying to spot the rule in a number pattern requires a bit of detective work. First, work out the difference between consecutive terms. If the difference is always the same, then you know the rule has something to do with this times table. For example, if the difference is always 4, then the rule is linked to the 4 times table, which we write as 4n.

The next stage is to compare this times table with your number pattern. Ask yourself, what do you do to the times table to get the number pattern?

If the answer is ‘add 3’, then add this to your rule. This will give a rule that looks something like 4n + 3.

Writing the rule for more complex patterns can be quite hard, but it is often easy to spot what is going on. A famous pattern is the Fibonacci sequence, where each successive term is created by adding the two previous. This sequence appears in many forms in nature, such as the pattern formed in sunflower seeds or the scales on a pineapple.