06/04/2020 (2011: National Sprint Round, Problem 13)

Q: The function f is defined by f(n) = f(n + 1) + f(n + 2), with f(1) = 0 and f(3) = 4. What is the value of f(4)?

A: -8

We first find out what f(2) is, because f(2) = f(3) + f(4). We solve for f(2) by using the equation: f(1) = f(2) + f(3), which simplifies to: 0 = f(2) + 4.

That simplifies to -4 = f(2)

We substitute -4 = f(2) and f(3) = 4 into the equation f(2) = f(3) + f(4) and we get: -4 = 4 + f(4)

We simplify that and we get: -8 = f(4)