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?

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.**View the archive of all weekly problems grouped by curriculum topic*

View the current weekly problem