In 24-34, F a , F 1 , F 2 , ... is the Fibonacci sequence. The Fibonacci sequence satisfies the recurrence relation F k = F k − 1 + F k − 2 , For every integer k ≥ 2. a. Explain why the following is true: F k + 1 = F k + F k − 1 for each integer k ≥ 1. b. Write an equation expressing F k + 2 in terms of F k + 1 and F k . c. Write an equation expressing F k + 3 in terms F k + 2 and F k + 1.
In 24-34, F a , F 1 , F 2 , ... is the Fibonacci sequence. The Fibonacci sequence satisfies the recurrence relation F k = F k − 1 + F k − 2 , For every integer k ≥ 2. a. Explain why the following is true: F k + 1 = F k + F k − 1 for each integer k ≥ 1. b. Write an equation expressing F k + 2 in terms of F k + 1 and F k . c. Write an equation expressing F k + 3 in terms F k + 2 and F k + 1.
Solution Summary: The author explains that the Fibonacci sequence satisfy the recurrence relation for all integers kge 1.
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