[tex]\bf \qquad \qquad \textit{sum of a finite arithmetic sequence} \\\\ S_n=\cfrac{n}{2}(a_1+a_n)\quad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\[-0.5em] \hrulefill\\ n=12\\ S_{12}=156 \end{cases}\implies 156=\cfrac{12}{2}(a_1+a_{12}) \\\\\\ 156=6(a_1+a_{12})\implies \cfrac{156}{6}=a_1+a_{12}\implies 26=a_1+a_{12}[/tex]
