UPSC NDA Math Model Paper 7

Given: The sum of first three terms of a GP is 13/12 and their product is - 1.
Let

a

r

,a,ar be the first three terms of the given GP.
⇒

a

r

+a+ar=

13

12

.......(1)
⇒

a

r

.a.ar=−1 .........(2)
From (2), we get a3=−1⇒a=−1
By substituting a = - 1 in equation (1), we get
⇒−

1

r

−1−r=

13

12

⇒12r2+25r+12=0
⇒ r = - 4/3 or r = - 3/4
Case 1: When a = - 1 and r = - 4/3
Then these three terms are: 3/4, - 1, 4/3
Case 2: When a = - 1 and r = - 3/4
Then these three terms are: 4/3, - 1, 3/4
Hence, in either case these three are: - 1, 3/4, 4/3