Write the sum $LaTeX: \displaystyle 36+40+44 \ldots +148+152$ in sigma notation and then find the sum.

The common difference is given by $LaTeX: \displaystyle a_2-a_1=40-(36)=4$ . Using the first term gives the sequene $LaTeX: \displaystyle a_n= 36+(n-1)(4)$ . Setting the general term equal to the last term and solving for $LaTeX: \displaystyle n$ gives $LaTeX: \displaystyle 36+(n-1)(4)=152 \implies n = 30$ . Writing in sigma notation gives $LaTeX: \displaystyle \displaystyle \sum_{n=1}^{30} \left(4 n + 32\right)$ . Using the formula for a finite arithmetic sum gives $LaTeX: \displaystyle \frac{ 30(36+152) }{2}=2820$ .