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

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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