# 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

##### Stage: 4 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

##### Stage: 4 and 5 Challenge Level:

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

### Difference Dynamics

##### Stage: 4 and 5 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

##### Stage: 5 Short Challenge Level:

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

### Black Box

##### Stage: 5 Challenge Level:

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