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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