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Consider the Fibonacci sequence of numbersf {a i }= 0;1,1,2,3,5,8...... where a i =a i-1 + a i-2 , a 0 = 0, and a
Consider the Fibonacci sequence of numbersf {ai}= 0;1,1,2,3,5,8...... where ai =ai-1 + ai-2, a0 = 0, and a1 = 1. The sequence gives rise to a beautiful spiral that appears everywhere in nature, see the images at the end of the assignment. Prove by induction that every third number in the Fibonacci sequence is even, e.g., for any i >= 1 it holds that a3i is an even number. For example,a3 ,a6 , a9 , etc. are all even numbers
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