Question

The sum of the first 12 terms of an arithmetic progression is 156. What is the sum of the first and twelfth terms?

Answer 1

`\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)`