Write the sum $LaTeX: \displaystyle 18+26+34 \ldots +250+258$ in sigma notation and then find the sum.

The common difference is given by $LaTeX: \displaystyle a_2-a_1=26-(18)=8$ . Using the first term gives the sequene $LaTeX: \displaystyle a_n= 18+(n-1)(8)$ . Setting the general term equal to the last term and solving for $LaTeX: \displaystyle n$ gives $LaTeX: \displaystyle 18+(n-1)(8)=258 \implies n = 31$ . Writing in sigma notation gives $LaTeX: \displaystyle \displaystyle \sum_{n=1}^{31} \left(8 n + 10\right)$ . Using the formula for a finite arithmetic sum gives $LaTeX: \displaystyle \frac{ 31(18+258) }{2}=4278$ .