Chapter 5.2, Problem 33ES

Find a formula in $n,a,m,$ and d for the um $\left(a+md\right)+\left(a+\left(m+1\right)d\right)+\left(a+\left(m+2\right)d\right)+\mathrm{...}+\left(a+\left(m+n\right)d\right)$ , where m and n are integers $n\ge 0$ and a and b are real numbers, Justify ypur answer.