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.

Summing Consecutive Numbers 

Age 11 to 14 Challenge Level:
Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

Shifting Times Tables 

Age 11 to 14 Challenge Level:
Can you find a way to identify times tables after they have been shifted up?

Charlie's Delightful Machine 

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.