Write the sum $LaTeX: \displaystyle -11-9-7 \ldots +65+67$ in sigma notation and then find the sum.

The common difference is given by $LaTeX: \displaystyle a_2-a_1=-9-(-11)=2$ . Using the first term gives the sequene $LaTeX: \displaystyle a_n= -11+(n-1)(2)$ . Setting the general term equal to the last term and solving for $LaTeX: \displaystyle n$ gives $LaTeX: \displaystyle -11+(n-1)(2)=67 \implies n = 40$ . Writing in sigma notation gives $LaTeX: \displaystyle \displaystyle \sum_{n=1}^{40} \left(2 n - 13\right)$ . Using the formula for a finite arithmetic sum gives $LaTeX: \displaystyle \frac{ 40(-11+67) }{2}=1120$ .