Fibonacci sequence The famous Fibonacci sequence was pro- posed by Leonardo Pisano, also known as Fibonacci, in about A.D. 1200 as a model for the growth of rabbit populations. It is given by the recurrence relation f,+1= f, + fp-1» for n = 1, 2, 3, ..., where fo = 1 and fj = 1. Each term of the sequence is the sum of its two predecessors. %3D a. Write out the first ten terms of the sequence. b. Is the sequence bounded? fa+1 c. Estimate or determine o = lim - fn ,the ratio of the successive terms of the sequence. Provide evidence that 1+ V5 , a number known as the golden mean. 2 d. Use induction to verify the remarkable result that (9" – (-1)"g"). V5

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