Write the sum $LaTeX: \displaystyle 4+8+12 \ldots +108+112$ in sigma notation and then find the sum.

The common difference is given by $LaTeX: \displaystyle a_2-a_1=8-(4)=4$ . Using the first term gives the sequene $LaTeX: \displaystyle a_n= 4+(n-1)(4)$ . Setting the general term equal to the last term and solving for $LaTeX: \displaystyle n$ gives $LaTeX: \displaystyle 4+(n-1)(4)=112 \implies n = 28$ . Writing in sigma notation gives $LaTeX: \displaystyle \displaystyle \sum_{n=1}^{28} 4 n$ . Using the formula for a finite arithmetic sum gives $LaTeX: \displaystyle \frac{ 28(4+112) }{2}=1624$ .