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# Sequences and Series

### Circles Ad Infinitum

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Age 16 to 18

Challenge Level

A circle is inscribed in an equilateral triangle. Smaller circles touch it and the sides of the triangle, the process continuing indefinitely. What is the sum of the areas of all the circles?

Age 16 to 18

Challenge Level

Can you work through these direct proofs, using our interactive proof sorters?

Age 16 to 18

Challenge Level

Watch the video to see how to add together an arithmetic sequence of numbers efficiently.

Age 16 to 18

ShortChallenge Level

What can you deduce about prime numbers in arithmetic progression?

Age 16 to 18

ShortChallenge Level

Can you work out what happens when this mad robot sets off?

Age 16 to 18

ShortChallenge Level

An arithmetic progression is shifted and shortened, but its sum remains the same...

Age 14 to 18

Challenge Level

A short challenge concerning the decay of medicines in the body.