Write the sum $LaTeX: \displaystyle 17+26+35 \ldots +386+395$ in sigma notation and then find the sum.

The common difference is given by $LaTeX: \displaystyle a_2-a_1=26-(17)=9$ . Using the first term gives the sequene $LaTeX: \displaystyle a_n= 17+(n-1)(9)$ . Setting the general term equal to the last term and solving for $LaTeX: \displaystyle n$ gives $LaTeX: \displaystyle 17+(n-1)(9)=395 \implies n = 43$ . Writing in sigma notation gives $LaTeX: \displaystyle \displaystyle \sum_{n=1}^{43} \left(9 n + 8\right)$ . Using the formula for a finite arithmetic sum gives $LaTeX: \displaystyle \frac{ 43(17+395) }{2}=8858$ .