Write the sum $LaTeX: \displaystyle 24+28+32 \ldots +116+120$ in sigma notation and then find the sum.

The common difference is given by $LaTeX: \displaystyle a_2-a_1=28-(24)=4$ . Using the first term gives the sequene $LaTeX: \displaystyle a_n= 24+(n-1)(4)$ . Setting the general term equal to the last term and solving for $LaTeX: \displaystyle n$ gives $LaTeX: \displaystyle 24+(n-1)(4)=120 \implies n = 25$ . Writing in sigma notation gives $LaTeX: \displaystyle \displaystyle \sum_{n=1}^{25} \left(4 n + 20\right)$ . Using the formula for a finite arithmetic sum gives $LaTeX: \displaystyle \frac{ 25(24+120) }{2}=1800$ .