The weighted A.M of first n natural numbers whose weights are equal to the corresponding numbers is equal to
2n+1
122n+1
132n+1
2n+16
The required mean is
X¯=1⋅1+2⋅2+3⋅3+…+n⋅n1+2+3+…+n=Σn2Σn=n(n+1)(2n+1)6n(n+1)2=2n+13