Describing patterns and sequences

problem
Mean sequence

Age

11 to 14

Challenge level

Weekly Problem 38 - 2009
This sequence is given by the mean of the previous two terms. What is the fifth term in the sequence?
problem
Expanding pattern

Age

11 to 14

Challenge level

How many squares are needed to continue this pattern?
problem
Many Matildas

Age

11 to 14

Challenge level

MatildaMatildaMatil... What is the 1000th letter?
problem
Paving paths

Age

11 to 14

Challenge level

How many different ways can I lay 10 paving slabs, each 2 foot by 1 foot, to make a path 2 foot wide and 10 foot long from my back door into my garden, without cutting any of the paving slabs?
problem
Sept 03

Age

11 to 14

Challenge level

What is the last digit of the number 1 / 5^903 ?
problem
Sept03 Sept03 Sept03

Age

7 to 11

Challenge level

This number has 903 digits. What is the sum of all 903 digits?
problem
Archimedes and numerical roots

Age

14 to 16

Challenge level

The problem is how did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?
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
Lastly - well

Age

11 to 14

Challenge level

What are the last two digits of 2^(2^2003)?
problem
Expanding zeros

Age

11 to 14

Challenge level

Weekly Problem 22 - 2008
The following sequence continues indefinitely... Which of these integers is a multiple of 81?