Q. 34.2( 5 Votes )
The sum of first three terms of a G.P. is 
, and their product is – 1. Find the G.P.
Answer :
Let the three numbers be 
.
∴ According to the question
⇒ 
…(1)
⇒ 
…(2)
From 2 we get
⇒ a3 = – 1
∴ a = – 1.
From 1 we get
⇒ 
⇒ 12a + 12ar + 12ar2 = 13r …(3)
Substituting a = – 1 in 3 we get
⇒ 12( – 1) + 12( – 1)r + 12( – 1)r2 = 13r
⇒12r2 + 25r + 12 = 0
⇒ 12r2 + 16r + 9r + 12 = 0…(4)
⇒ 4r(3r + 4) + 3(3r + 4) = 0
∴ r = 
or r = 
∴ Now the equation will be
⇒ 
⇒ 
∴ The three numbers are 
.
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