Write the sum $LaTeX: \displaystyle -24-22-20 \ldots +48+50$ in sigma notation and then find the sum.

The common difference is given by $LaTeX: \displaystyle a_2-a_1=-22-(-24)=2$ . Using the first term gives the sequene $LaTeX: \displaystyle a_n= -24+(n-1)(2)$ . Setting the general term equal to the last term and solving for $LaTeX: \displaystyle n$ gives $LaTeX: \displaystyle -24+(n-1)(2)=50 \implies n = 38$ . Writing in sigma notation gives $LaTeX: \displaystyle \displaystyle \sum_{n=1}^{38} \left(2 n - 26\right)$ . Using the formula for a finite arithmetic sum gives $LaTeX: \displaystyle \frac{ 38(-24+50) }{2}=494$ .