Question

What is the sum of a 54-term arithmetic sequence where the first term is 6 and the last term is 377

Answer 1

`\bf \textit{sum of a finite arithmetic sequence} \\\\ S_n=\cfrac{n(a_1+a_n)}{2}\qquad \begin{cases} n=n^(th)\ term\\ a_1=\textit{first term's value}\\ ----------\\ n=54\\ a_1=6\\ a_(54)=377 \end{cases} \\\\\\ S_(54)=\cfrac{54(6+377)}{2}\implies S_(54)=\cfrac{54(383)}{2} \\\\\\ S_(54)=\cfrac{2062}{2}\implies S_(54)=10341`