Write the sum $LaTeX: \displaystyle 44+36+28 \ldots -212-220$ in sigma notation and then find the sum.

The common difference is given by $LaTeX: \displaystyle a_2-a_1=36-(44)=-8$ . Using the first term gives the sequene $LaTeX: \displaystyle a_n= 44+(n-1)(-8)$ . Setting the general term equal to the last term and solving for $LaTeX: \displaystyle n$ gives $LaTeX: \displaystyle 44+(n-1)(-8)=-220 \implies n = 34$ . Writing in sigma notation gives $LaTeX: \displaystyle \displaystyle \sum_{n=1}^{34} \left(52 - 8 n\right)$ . Using the formula for a finite arithmetic sum gives $LaTeX: \displaystyle \frac{ 34(44-220) }{2}=-2992$ .