Write the sum $LaTeX: \displaystyle 17+25+33 \ldots +385+393$ in sigma notation and then find the sum.

The common difference is given by $LaTeX: \displaystyle a_2-a_1=25-(17)=8$ . Using the first term gives the sequene $LaTeX: \displaystyle a_n= 17+(n-1)(8)$ . Setting the general term equal to the last term and solving for $LaTeX: \displaystyle n$ gives $LaTeX: \displaystyle 17+(n-1)(8)=393 \implies n = 48$ . Writing in sigma notation gives $LaTeX: \displaystyle \displaystyle \sum_{n=1}^{48} \left(8 n + 9\right)$ . Using the formula for a finite arithmetic sum gives $LaTeX: \displaystyle \frac{ 48(17+393) }{2}=9840$ .