List

Sequences and Series

Circles ad infinitum
problem
Favourite

Circles ad infinitum

Age
16 to 18
Challenge level
filled star filled star empty star
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
problem
Favourite

Direct logic

Age
16 to 18
Challenge level
filled star empty star empty star
Can you work through these direct proofs, using our interactive proof sorters?
Prime APs
problem

Prime APs

Age
16 to 18
Challenge level
filled star empty star empty star
What can you deduce about prime numbers in arithmetic progression?
Mad robot
problem

Mad robot

Age
16 to 18
Challenge level
filled star empty star empty star
Can you work out what happens when this mad robot sets off?
AP train
problem

AP train

Age
16 to 18
Challenge level
filled star empty star empty star
An arithmetic progression is shifted and shortened, but its sum remains the same...
Medicine half life
problem

Medicine half life

Age
14 to 18
Challenge level
filled star empty star empty star
A short challenge concerning the decay of medicines in the body.
Speedy summations
problem

Speedy summations

Age
16 to 18
Challenge level
filled star empty star empty star

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