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**muddywaters** Given the arithmetic sequence $\displaystyle -5,a_1,a_2, ... ,a_n,15 $, and the sum of its first $\displaystyle n+2 $ terms is $\displaystyle 100 $, find $\displaystyle n$.

My question is this:

the $\displaystyle \frac{(n+2)(-5+15)}{2} $ part is from $\displaystyle \frac{n(a+l)}{2}$, where $\displaystyle n$ is the number of terms, $\displaystyle a$ is the first term and $\displaystyle l$ is the last term.

In this case, for the sum of $\displaystyle n+2$ terms, the last term is the $\displaystyle (n+2)_t_h$term. the answer uses $\displaystyle 15$, which is the $\displaystyle (n+1)_t_h$ term, since it's directly after the $\displaystyle n_t_h$ term. it's not the $\displaystyle (n+2)_t_h$ term. why is it like that? did i misunderstand something??