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  • Early Years Foundation Stage

Starting Fibonacci

Age 11 to 14
ShortChallenge Level Yellow star
Secondary curriculum
  • Problem
  • Solutions

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.

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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