$\begin{align} & \sum\nolimits_{r=1}^{n}{(5r-7)} \\ & {{U}_{1}}=5(1)-7=-2 \\ & {{U}_{2}}=5(2)-7=3 \\ & {{U}_{3}}=5(3)-7=8 \\ & {{S}_{n}}=\frac{n}{2}\left[ 2a+(n-1)d \right] \\ & a=-2,d=5 \\ & {{S}_{n}}=\frac{n}{2}\left[ 2(-2)+(n-1)5 \right] \\ & {{S}_{n}}=\frac{n}{2}\left[ 5n-9 \right] \\\end{align}$