Write the sum $LaTeX: \displaystyle 28+30+32 \ldots +106+108$ in sigma notation and then find the sum.

The common difference is given by $LaTeX: \displaystyle a_2-a_1=30-(28)=2$ . Using the first term gives the sequene $LaTeX: \displaystyle a_n= 28+(n-1)(2)$ . Setting the general term equal to the last term and solving for $LaTeX: \displaystyle n$ gives $LaTeX: \displaystyle 28+(n-1)(2)=108 \implies n = 41$ . Writing in sigma notation gives $LaTeX: \displaystyle \displaystyle \sum_{n=1}^{41} \left(2 n + 26\right)$ . Using the formula for a finite arithmetic sum gives $LaTeX: \displaystyle \frac{ 41(28+108) }{2}=2788$ .