\(\renewcommand{\d}{\displaystyle}\newcommand{\N}{\mathbb N}\)

Suppose [math]f:\N \to \N satisfies the recurrence [math]f(n+1) = f(n) + 3\text{.} Note that this is not enough information to define the function, since we don’t have an initial condition. For each of the initial conditions below, find the value of [math]f(5)\text{.}

- [math]
f(0) = 0\text{.} [math]f(5) = - [math]
f(0) = 1\text{.} [math]f(5) = - [math]
f(0) = 2\text{.} [math]f(5) = - [math]
f(0) = 100\text{.} [math]f(5) =