Solving a recurrence relation (homework) Solve the following recurrence relation:
$$l(n+1)=l(n)+π(4+2cn), \quad n=0,1,2,3,\ldots$$

You can rewrite the equation as:
$$
l(n + 1) - l(n) = \pi(4 + 2 c n)
$$
Thus:
$$
\begin{align*}
\sum_{0 \le k < n} (l(k + 1) - l(k))
  &= \sum_{0 \le k < n} \pi(4 + 2 c k) \\
l(n)
  &= l(0) + \sum_{0 \le k < n} \pi(4 + 2 c k)
\end{align*}
$$
Your recurrence is linear, al right.
