Geometric sequences

problem
Favourite

Magic Plant

Age

5 to 7

Challenge level

2 out of 3

On Friday the magic plant was only 2 centimetres tall. Every day it doubled its height. How tall was it on Monday?
problem
Favourite

The Amazing Splitting Plant

Age

5 to 7

Challenge level

3 out of 3

Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?
problem
Favourite

The Tomato and the Bean

Age

5 to 7

Challenge level

3 out of 3

At the beginning of May, Tom put his tomato plant outside. On the same day he sowed a bean in another pot. When will the two be the same height?
problem
Favourite

Pocket Money

Age

11 to 14

Challenge level

1 out of 3

Which of these pocket money systems would you rather have?
problem
Favourite

Tower of Hanoi

Age

11 to 14

Challenge level

2 out of 3

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

Double Trouble

Age

14 to 16

Challenge level

1 out of 3

Simple additions can lead to intriguing results...
problem
Favourite

Tiny Nines

Age

14 to 16

Challenge level

2 out of 3

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

Summing Geometric Progressions

Age

14 to 18

Challenge level

1 out of 3

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

Sixty-Seven Squared

Age

16 to 18

Challenge level

1 out of 3

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
Favourite

Clickety Click and All the Sixes

Age

16 to 18

Challenge level

1 out of 3

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