The sum of first n terms of a certain series is given as 2n2-3n . Show that the series is an A.P.

The sum of first n terms of a certain series is given as 2n2-3n . Show that the series is an A.P.
Solution :
Given that :
tn  = 2n2 - 3n
tn  = 2n2 - 3n
n = 1
t1  = 2(1)2 - 3(1)
  =   2 - 3  
 t =  -1 =  a
n = 2
t2  = 2(2)2 - 3(2)
  =   8 - 6  
 t =  2
d  = 2 - (-1)  = 3
Sn  = (n/2) [2a + (n - 1)d]
Sn  = (n/2) [2(-1) + (n - 1)3]
  =  (n/2) [-2 + 3n - 3]
  =  (n/2) [3n - 5]

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