The sum of first three terms of a G.P is 39/10 and their product is 1. Find the common ratio and the terms

Solution:

Let a/r, a, ar be the first three terms of the G.P.

It is given that a/r + a + ar = 39/10 ....(1)

(a/r) (a) (ar) = 1 ....(2)

From (2), we obtain

a³ = 1

⇒ a = 1 (considering real roots)

Substituting a = 1 in (1), we obtain

⇒ 1/r + 1 + r = 39/10

⇒ 1 + r + r² = 39/10 r

⇒ 10 + 10r + 10r² - 39r = 0

⇒ 10r² - 29r + 10 = 0

⇒ 10r² - 25r - 4r + 10 = 0

⇒ 5r (2r - 5) - 2 (2r - 5) = 0

⇒ (5r - 2)(2r - 5) = 0

r = 2/5, 5/2

Thus, the three terms of the G.P are 2/5, 5/2

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NCERT Solutions Class 11 Maths Chapter 9 Exercise 9.3 Question 12

The sum of first three terms of a G.P is 39/10 and their product is 1. Find the common ratio and the terms

Summary:

It is given that the sum of first three terms of a G.P is 39/10 and their product is 1. Thus, the common ratio is 2/5, 5/2