show that

$\displaystyle \displaystyle\sum_{r=1}^n \frac{r+3}{2} = kn(n+7) $

where K is a rational constant to be found

so I just plug in numbers for 'r' e.g. r=1,2,3 , n and get the sequence 2, 5/2 , 3 ,.....$\displaystyle \frac{ n+3}{2} $

but not sure how to prove it equals the expression $\displaystyle kn(n+7) $