\(\bf the\ n^{th}\textit{ term of an arithmetic sequence}\\\\
a_n=a_1(n-1)d\qquad
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term}\\
d=\textit{common difference}
\end{cases}\\\\
-----------------------------\\\\
\textit{Sum of a finite arithmetic sequence}\\\\
S_n=\cfrac{n}{2}(a_1+a_n)\qquad
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term}\\
\end{cases}\\\\
-----------------------------\\\\
S_{12}\impliedby \textit{means n = 12}\qquad thus
\\\\\\\)
\(\bf S_{12}=\cfrac{12}{2}(7+a_{12})\impliedby \textit{so what's }a_{12}?\qquad well
\\\\\\
a_{12}=7(12-1)(-8)\)
