Write the sum $LaTeX: \displaystyle 36+28+20 \ldots -236-244$ in sigma notation and then find the sum.

The common difference is given by $LaTeX: \displaystyle a_2-a_1=28-(36)=-8$ . Using the first term gives the sequene $LaTeX: \displaystyle a_n= 36+(n-1)(-8)$ . Setting the general term equal to the last term and solving for $LaTeX: \displaystyle n$ gives $LaTeX: \displaystyle 36+(n-1)(-8)=-244 \implies n = 36$ . Writing in sigma notation gives $LaTeX: \displaystyle \displaystyle \sum_{n=1}^{36} \left(44 - 8 n\right)$ . Using the formula for a finite arithmetic sum gives $LaTeX: \displaystyle \frac{ 36(36-244) }{2}=-3744$ .