Thanks Guest,
Firstly this is not an AP
3*1^2+4*2^2+5*3^2+...............+(n+2)*n^2 is a A.P series. Find the sumtotal.
I put this into Wolfram|alpha and got this result.
https://www.wolframalpha.com/input/?i=sum+of+(k%2B2)*k%5E2+from+k%3D1+to+n
I do not know how to do this without Wolfram|alpha though.
I have seen Geno314 do questions along this line but I have not learned his technique :///