S(n): 2+7+12+...+(5n+2) = 1/2(n+1)(5n+4)

S(1): LHS (5(1)+2) = 9

RHS 1/2(1+1)(5(1)+4) = 9 RHS = LHS

Assume True: S(k) = 2+7+12+...+(5k+2) = 1/2(k+1)(5k+4)

Want to Show True: S(k+1) = 2+7+12+...+(5(k+1)+2) = 1/2((k+1)+1)(5(k+1)+4)

Here's what I have so far.

LHS = 2+7+12+...+ (5k+2) + (5(k+1)+2) = 5(k+1)+ 2 + 1/2(k+1)(5k+4) by induction hypothesis

I am stuck here...if anyone can help I appreciate it.