
Suppose $f:\N \to \N$ satisfies the recurrence $f(n+1) = f(n) + 3\text{.}$ 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 $f(5)\text{.}$
1. $f(0) = 0\text{.}$
$f(5) =$
2. $f(0) = 1\text{.}$
$f(5) =$
3. $f(0) = 2\text{.}$
$f(5) =$
4. $f(0) = 100\text{.}$
$f(5) =$