Question

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 1

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.
This is also equal to 617.
182 + 3a = 617 => a = 145
f(10) = f(12) - f(11) = 145 - 91 = 54.