Write the sum $LaTeX: \displaystyle 26+32+38 \ldots +248+254$ 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 $LaTeX: \displaystyle 26+(n-1)(6)=254 \implies n = 39$ . Writing in sigma notation gives $LaTeX: \displaystyle \displaystyle \sum_{n=1}^{39} \left(6 n + 20\right)$ . Using the formula for a finite arithmetic sum gives $LaTeX: \displaystyle \frac{ 39(26+254) }{2}=5460$ .