Finding the closed form of a summation when i is 0

Question

I am trying to find the closed form summation of this:

$$\sum_{i=0}^{n-1} (5 + 2n + i) $$

Here I tried to break up the terms but I know that I'm doing something wrong by not accounting for $i=0$

I did this to begin and I know it is wrong...

$$\ 5(n-1) + 2n(n-1) + \frac{(n(n-1)}{2}$$

If I could get help getting started with this first step by converting in terms of n I think I could figure the rest out.

Answer 1

You've done pretty well. The only problem is that there are $n$ terms (counting the $i = 0$ term as the first term), so the sum should be $$5n + 2n^2 + \frac{n(n - 1)}{2}.$$