Geometric sequences

problem
Tower of Hanoi

Age

11 to 14

Challenge level

The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.
problem
Double trouble

Age

14 to 16

Challenge level

Simple additions can lead to intriguing results...
problem
Tiny nines

Age

14 to 16

Challenge level

What do you notice about these families of recurring decimals?
problem
Geometric parabola

Age

14 to 16

Challenge level

Explore what happens when you draw graphs of quadratic equations with coefficients based on a geometric sequence.
problem
Summing geometric progressions

Age

14 to 18

Challenge level

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

Age

14 to 18

Challenge level

How can visual patterns be used to prove sums of series?
problem
Sixty-seven squared

Age

16 to 18

Challenge level

Evaluate these powers of 67. What do you notice? Can you convince someone what the answer would be to (a million sixes followed by a 7) squared?
problem
Clickety click and all the sixes

Age

16 to 18

Challenge level

What is the sum of: 6 + 66 + 666 + 6666 ............+ 666666666...6 where there are n sixes in the last term?
problem
Converging product

Age

16 to 18

Challenge level

In the limit you get the sum of an infinite geometric series. What about an infinite product (1+x)(1+x^2)(1+x^4)... ?
problem
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?