Geometric sequences

problem
Vanishing point

Age

14 to 18

Challenge level

How can visual patterns be used to prove sums of series?
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
Double trouble

Age

14 to 16

Challenge level

Simple additions can lead to intriguing results...
problem
Clickety click

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
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
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
Mobile numbers

Age

5 to 11

Challenge level

In this investigation, you are challenged to make mobile phone numbers which are easy to remember. What happens if you make a sequence adding 2 each time?
problem
Production equation

Age

16 to 18

Challenge level

Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
problem
Investigating Pascal's triangle

Age

7 to 11

Challenge level

In this investigation, we look at Pascal's Triangle in a slightly different way - rotated and with the top line of ones taken off.
problem
Von Koch curve

Age

16 to 18

Challenge level

Make a poster using equilateral triangles with sides 27, 9, 3 and 1 units assembled as stage 3 of the Von Koch fractal. Investigate areas & lengths when you repeat a process infinitely often.