Write the sum $LaTeX: \displaystyle -16-10-4 \ldots +104+110$ in sigma notation and then find the sum.

The common difference is given by $LaTeX: \displaystyle a_2-a_1=-10-(-16)=6$ . Using the first term gives the sequene $LaTeX: \displaystyle a_n= -16+(n-1)(6)$ . Setting the general term equal to the last term and solving for $LaTeX: \displaystyle n$ gives $LaTeX: \displaystyle -16+(n-1)(6)=110 \implies n = 22$ . Writing in sigma notation gives $LaTeX: \displaystyle \displaystyle \sum_{n=1}^{22} \left(6 n - 22\right)$ . Using the formula for a finite arithmetic sum gives $LaTeX: \displaystyle \frac{ 22(-16+110) }{2}=1034$ .