Write the sum $LaTeX: \displaystyle 11+3-5 \ldots -357-365$ in sigma notation and then find the sum.

The common difference is given by $LaTeX: \displaystyle a_2-a_1=3-(11)=-8$ . Using the first term gives the sequene $LaTeX: \displaystyle a_n= 11+(n-1)(-8)$ . Setting the general term equal to the last term and solving for $LaTeX: \displaystyle n$ gives $LaTeX: \displaystyle 11+(n-1)(-8)=-365 \implies n = 48$ . Writing in sigma notation gives $LaTeX: \displaystyle \displaystyle \sum_{n=1}^{48} \left(19 - 8 n\right)$ . Using the formula for a finite arithmetic sum gives $LaTeX: \displaystyle \frac{ 48(11-365) }{2}=-8496$ .