The Fibonacci sequence satisfies the recurrence relation
Chapter 5, Problem 25E(choose chapter or problem)
Problem 25E
The Fibonacci sequence satisfies the recurrence relation Fk = Fk-1 + Fk–2, for all integers k ≥ 2.
a. Explain why the following is true:
Fk+1 = Fk + Fk–1 for all integers k ≥ 1.
b. Write an equation expressing Fk+2 in terms of Fk+1 and Fk.
c. Write an equation expressing Fk+3 in terms of Fk+2 and Fk+1
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