Question

10. If the sum of first n terms in a series is given by 2nsquare+ 3n the series is in
(a) A.P.
(b) G.P.
(c) H.P.
(d) None
With explanation pls​

Answer 1

The series is In A.P

Explain.

Given Sn= 2n^2 - 3n

(put n=1)

S1= 2-3 = -1

so, t1= a = -1

(Put n=2)

S2= 2× 2^2 - 3 × 2

S2 = 2

so, t2= S2- S1 = 2 - (-1) = 3

and d= t2- t1 = 3+1=4

(Put n=3)

S3= 2× 3^2 - 3 × 3

S3= 9

so, t3= S3-S2 = 9 - 2 = 7

and d= t3- t2 = 7-3 =4

so clearly it's a A.P series

with a= -1 and d = 4