Relations Functions

If f(x + 2) = f(x) + f(x + 1) for all positive integers x, and f(11) = 91, f(15) = 617, then f(10) equals

Answer

f(x+2) = f(x) + f(x+1)

f(11) = 91

Let f(12) = a

f(13) = 91 + a

f(14) = 91 + 2a

f(15) = 182 + 3a.

617 = 182 + 3a

a = 145

f(10) = f(12) - f(11)

= 145 - 91

= 54

The correct answer is 54.