Write the sum $LaTeX: \displaystyle -26-34-42 \ldots -234-242$ in sigma notation and then find the sum.

The common difference is given by $LaTeX: \displaystyle a_2-a_1=-34-(-26)=-8$ . Using the first term gives the sequene $LaTeX: \displaystyle a_n= -26+(n-1)(-8)$ . Setting the general term equal to the last term and solving for $LaTeX: \displaystyle n$ gives $LaTeX: \displaystyle -26+(n-1)(-8)=-242 \implies n = 28$ . Writing in sigma notation gives $LaTeX: \displaystyle \displaystyle \sum_{n=1}^{28} \left(- 8 n - 18\right)$ . Using the formula for a finite arithmetic sum gives $LaTeX: \displaystyle \frac{ 28(-26-242) }{2}=-3752$ .