Class 11

Math

Algebra

Sequences and Series

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.

- 6

$S_{n}=3n_{2}$ 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 $3,9,15,21....$