$$S=\frac{n}{2}(a+1)$$
$S=\frac{n\left(a+1\right)}{2}$
$\left\{\begin{matrix}a=\frac{2S}{n}-1\text{, }&n\neq 0\\a\in \mathrm{R}\text{, }&S=0\text{ and }n=0\end{matrix}\right.$
