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## 'Weekly Problem 40 - 2012' printed from http://nrich.maths.org/

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 (not necessarily 1 and 1) 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?

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*This problem is taken from the UKMT Mathematical Challenges.*

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