Chapter 13, Problem 14E

Consider the following sequence of equations involving Fibonacci numbers.

$2\left(2\right)-3=12\left(3\right)-5=12\left(5\right)-8=22\left(8\right)-13=3⋮$

a. Write down a reasonable choice for the fifth equation in this sequence.

b. Find the subscript that will make the following equation true.

$2\left(F_{?}\right)-F_{15}=F_{12}$

c. Find the subscript that will make the following equation true.

$2\left(F_{N+2}\right)-F_{N+3}=F$