Find the sum to 'n' terms of the series `3xx8+6xx11+9xx14+…....`

Explanation

`n^ th ` term of the given series `=3 n xx(5+3 n)=15 n+9 n^2`

`S_n=sum_k=1^n(15 k+9 k^2)=sum_k=1^n 15 k+sum_k=1^n 9 k^2=15 n(n+1)/2+9 n(n+1)(2 n+1)/6`

`=n(n+1)/6 cdot[45+9(2 n+1)]=n(n+1)/6[18 n i+54]=3 n(n+1)(n+3)`