Question

the sum of n terms of an AP IS 3n2 + 5n. the series is

Answer 1

sn=3n2+5n
so , s1=3*1*2+5*1
          =11
      s2=3*2*2+5*2
          =22
       s3=3*3*2+5*3
          =33
s1=t1=11
s2=t1+d=22
    =   d=22-11
           =11
d=11
AP:- 11,22,33

Answer 2

Given that, 

$S_n = 3n^2 + 5n$

We know that,

$t_n = S_n - S_(n-1)$

$t_n = 3n^2 + 5n - [3(n-1)^2 + 5(n-1)]$

$t_n = 3n^2 + 5n - [3n^2-6n+3 + 5n-5]$

$t_n = 3n^2 + 5n - 3n^2 + 6n - 3 - 5n + 5$

$t_n = 6n + 2$

The series is 

6(1) + 2, 6(2)+2, 6(3)+2, 6(4)+2
⇒ 8, 14, 20, 26 ........