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### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Sequences and Series

### A Little Light Thinking

### Summing Geometric Progressions

### Difference Dynamics

### Mad Robot

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Age 14 to 16

Challenge Level

This problem encourages students to think about the properties of numbers. It could be used to consolidate work on linear sequences.

Age 14 to 18

Challenge Level

This problem provides an introduction to summing geometric series, and allows students to discover for themselves the formulae used to calculate such sums.

Age 14 to 18

Challenge Level

This is an engaging investigation that quickly yields results and leads to conjectures and a lot of mathematical thinking and discussion.

Age 16 to 18

ShortChallenge Level

This short problem can be given to students who have been working on sequences or algorithms.