Here's a problem from tonight's homework that I am stuck on.

$\displaystyle 3+8+13+18+...+(5n-2)=\frac{n}{2}(5n+1)$

Here's the work I did up to the point I'm stuck:

$\displaystyle s_{1}=3=\frac{1}{2}[5(1)+1]\surd$

$\displaystyle s_{k}=3+8+13+18+...+(5n-2)=\frac{k}{2}(5k+1)$

$\displaystyle s_{k+1}=3+8+13+18+...+(5n-2)+[5(k+1)-2]$

$\displaystyle =s_{k}+(5k+3)$

$\displaystyle =\frac{k}{2}(5k+1)(5k+3)$

I know that $\displaystyle s_{k+1}$ is supposed to equal $\displaystyle \frac{k+1}{2}(5k+6)$ when it's all said and done. But at this point, I cannot figure out how to reach that.

I will greatly appreciate any and all help.