Question: 2014 Winter Midterm - 10
The function $f : \mathbb{N} \rightarrow \mathbb{N}$ is defined by
$$
\begin{align}
f(0) &= 2 \\
f(n + 1) &= f(n) + 6n - 2\; \ \mathrm{for}\ n \geq 0
\end{align}
$$
What is $f(n)$?
(a)
$f(n) = 2n^{2} + 5n + 2$
(b)
$f(n) = 3n^{2} + 5n + 2$
(c)
$f(n) = 2n^{2} - 5n + 2$
(d)
$f(n) = 3n^{2} - 5n + 2$