Q. 54.5( 2 Votes )

The sum of the first three terms of a G.P. is , and their product is 1. Find the common ratio and the terms.

Answer :

Let the three numbers be .


According to the question


…(1)


…(2)


From 2 we get


a3 = 1


a = 1.


From 1 we get



10a + 10ar + 10ar2 = 39r …(3)


Substituting a = 1 in 3 we get


10(1) + 10(1)r + 10(1)r2 = 39r


10r2 – 29r + 10 = 0


10r2 – 25r – 4r + 10 = 0…(4)


5r(2r – 5) – 2(2r – 5) = 0


r = or r =


Now the equation will be




The three numbers are.


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