# Patterns in Number Sequences

### Patterns in Number Sequences

Mathematicians are often interested in exploring the structure of number sequences. In these problems, we invite you to explore and describe sequences, and explain the patterns you notice.

##### Age 11 to 14

Challenge Level

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

##### Age 11 to 14

Challenge Level

Can you find a way to identify times tables after they have been shifted up or down?

##### Age 11 to 16

Challenge Level

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

Spotting patterns can be an important first step - explaining why it is appropriate to generalise is the next step, and often the most interesting and important.