Question

Find the common difference of an A.P. in which sum of any number of terms is always three times the squared number of these terms.

Answer 1

$S_n=3n^2$ by given condition

$T_n=S_n-S_{n-1}=3n^2-3{(n-1)}^2=6n-3$

Putting $n=1,2,3,..$

The series is $3,9,15,\mathrm{21....}$