Sequences and Series

Sequences and Series

Sequences are everywhere in mathematics! In these problems you can explore some sequences, learn how to represent them, and how to calculate sums of series.

A Little Light Thinking 

Age 14 to 16 Challenge Level:
Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?

Summing Geometric Progressions 

Age 14 to 18 Challenge Level:
Watch the video to see how to sum the sequence. Can you adapt the method to sum other sequences?

Difference Dynamics 

Age 14 to 18 Challenge Level:
Take three whole numbers. The differences between them give you three new numbers. Find the differences between the new numbers and keep repeating this. What happens?

Weekly Challenge 14: Mad Robot 

Age 16 to 18 Short Challenge Level:
A weekly challenge: these are shorter problems aimed at Post-16 students or enthusiastic younger students.

Black Box 

Age 16 to 18 Challenge Level:
This black box reveals random values of some important, but unusual, mathematical functions. Can you deduce the purpose of the black box?