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PROBLEMS

(10 pts) A program determines the position n of a particular number in the Fibonacci sequence. Fibonacci numbers F_n are defined by the recursive relation[1] below. It is assumed that the F_n provided is a valid Fibonacci number.

where the initial seeds are F₀ = 0 and F₁ = 1. The following table shows the position n of the first six numbers F_n in the Fibonacci sequence (including the seeds 0 and 1);

Position (n)	0	1	2	3	4	5
Fibonacci number (Fn)	0	1	1	2	3	5

The formula to calculate the position n of a Fibonacci number F_n in the Fibonacci sequence is:

is the golden ratio.

Equation (1) will be evaluated twice (i.e., once with +4, and once with -4) and only integer solutions can be used to represent the position n of a Fibonacci number F_n. (Hint: The logarithm change-of-base formula can help simplify complicated logarithm functions.)

[1] https://en.wikipedia.org/wiki/Fibonacci_number

A program determines the position n of a particular number in the Fibonacci sequence. Fibonacci numbers Fn are defined by the recursive relation[1] below. It is assumed that the Fn provided is a valid Fibonacci number. where the initial seeds are F_0 = 0 and F_1 = 1. The following table shows the position n of the first six numbers F_n in the Fibonacci sequence (including the seeds 0 and 1): The formula to calculate the position n of a Fibonacci number F_n in the Fibonacci sequence is: n = log_phi (F_n Squareroot 5 + Squareroot 5 F_n ^2 plusminus 4/2) is the golden ratio. phi = 1 + Squareroot 5/2 almostequalto 1.6180339887 .. Equation (1) will be evaluated twice (i.e., once with +4, and once with -4) and only integer solutions can be used to represent the position n of a Fibonacci number F_n