Question

How to find S12 of the following series

Answer 1

`\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)`