Write the sum $LaTeX: \displaystyle 26+32+38 \ldots +218+224$ in sigma notation and then find the sum.

The common difference is given by $LaTeX: \displaystyle a_2-a_1=32-(26)=6$ . Using the first term gives the sequene $LaTeX: \displaystyle a_n= 26+(n-1)(6)$ . Setting the general term equal to the last term and solving for $LaTeX: \displaystyle n$ gives $LaTeX: \displaystyle 26+(n-1)(6)=224 \implies n = 34$ . Writing in sigma notation gives $LaTeX: \displaystyle \displaystyle \sum_{n=1}^{34} \left(6 n + 20\right)$ . Using the formula for a finite arithmetic sum gives $LaTeX: \displaystyle \frac{ 34(26+224) }{2}=4250$ .