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# Starting Fibonacci

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Age 11 to 14

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The standard Fibonacci sequence 1, 1, 2, 3, 5, 8, 13, ... begins with two 1s and each later number in the sequence is the sum of the previous two numbers.

Other Fibonacci-like sequences can be constructed by starting with any two numbers a and b, and using the same rule for creating the other numbers in the sequence.

What is the first term of the Fibonacci-like sequence whose second term is 4 and whose fifth term is 22?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.

You can find more short problems, arranged by curriculum topic, in our short problems collection.

Imagine you are suspending a cube from one vertex and allowing it to hang freely. What shape does the surface of the water make around the cube?

Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.