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

⇒ a^{3} = 1

∴ a = 1.

From 1 we get

⇒

⇒ 10a + 10ar + 10ar^{2} = 39r …(3)

Substituting a = 1 in 3 we get

⇒ 10(1) + 10(1)r + 10(1)r^{2} = 39r

⇒10r^{2} – 29r + 10 = 0

⇒ 10r^{2} – 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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