UPSC NDA Math Model Paper 10

Lets three terms of GP be a/r, a, ar
Given: The product of first three terms of GP = 216 and their sum is 19
⇒

a

r

×a×ar=125⇒a3=216⇒a=6
According to second statement,
⇒

a

r

+a+ar=19 ⇒a(

1

r

+1+r)=19
Put the value of a=6 in the above equation
⇒6(

1

r

+1+r)=19
⇒6+6r+6r2=19r ⇒6r2−13r+6=0
⇒ (3r - 2) × (2r - 3) = 0
⇒ r = 2/3 or 3/2
As it is given that r > 1
Hence common ratio r = 3/2.