Sequences and Series

Circles Ad Infinitum

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?

Direct Logic

Age 16 to 18 Challenge Level:

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

Speedy Summations

Age 16 to 18 Challenge Level:

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

Prime Aps

Age 14 to 18 Short Challenge Level:

What can you deduce about prime numbers in arithmetic progression?

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.

AP Train

Age 16 to 18 Short Challenge Level:

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

Weekly Challenge 32: Medicine Half Life

Age 14 to 18 Challenge Level:

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