Sequences and Series

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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 link

A Little Light Thinking 

Stage: 4 Challenge Level: Challenge Level:1

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 link

Summing Geometric Progressions 

Stage: 4 and 5 Challenge Level: Challenge Level:1

Watch the video to see how to sum the sequence. Can you adapt the method to sum other sequences?

Difference Dynamics link

Difference Dynamics 

Stage: 4 and 5 Challenge Level: Challenge Level:1

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 link

Weekly Challenge 14: Mad Robot 

Stage: 5 Short Challenge Level: Challenge Level:1

A weekly challenge: these are shorter problems aimed at Post-16 students or enthusiastic younger students.

Black Box link

Black Box 

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

This black box reveals random values of some important, but unusual, mathematical functions. Can you deduce the purpose of the black box?