Write the sum $LaTeX: \displaystyle 11+16+21 \ldots +231+236$ in sigma notation and then find the sum.

The common difference is given by $LaTeX: \displaystyle a_2-a_1=16-(11)=5$ . Using the first term gives the sequene $LaTeX: \displaystyle a_n= 11+(n-1)(5)$ . Setting the general term equal to the last term and solving for $LaTeX: \displaystyle n$ gives $LaTeX: \displaystyle 11+(n-1)(5)=236 \implies n = 46$ . Writing in sigma notation gives $LaTeX: \displaystyle \displaystyle \sum_{n=1}^{46} \left(5 n + 6\right)$ . Using the formula for a finite arithmetic sum gives $LaTeX: \displaystyle \frac{ 46(11+236) }{2}=5681$ .