Write the sum $LaTeX: \displaystyle -18-26-34 \ldots -362-370$ in sigma notation and then find the sum.

The common difference is given by $LaTeX: \displaystyle a_2-a_1=-26-(-18)=-8$ . Using the first term gives the sequene $LaTeX: \displaystyle a_n= -18+(n-1)(-8)$ . Setting the general term equal to the last term and solving for $LaTeX: \displaystyle n$ gives $LaTeX: \displaystyle -18+(n-1)(-8)=-370 \implies n = 45$ . Writing in sigma notation gives $LaTeX: \displaystyle \displaystyle \sum_{n=1}^{45} \left(- 8 n - 10\right)$ . Using the formula for a finite arithmetic sum gives $LaTeX: \displaystyle \frac{ 45(-18-370) }{2}=-8730$ .