Question

Three numbers form an increasing GP. If the middle term is doubled, then the new numbers are in Ap. The common ratio of GP is
(a) 2 + √3
(b) 2 – √3
(c) 2 ± √3
(d) None of these​

Answer 1

Answer:

Three numbers form an increasing GP. If the middle term is doubled, then the new numbers are in Ap. The common ratio of GP is

$\rm\underline\bold{a)\:2 + √3 \red{\huge{\checkmark}}}$

(b) 2 – √3

(c) 2 ± √3

(d) None of these

Explanation

Let the three numbers be a/r, a, ar

Since the numbers form an increasing GP, So r > 1

Now, it is given that a/r, 2a, ar are in AP

⇒ 4a = a/r + ar

⇒ r² – 4r + 1 = 0

⇒ r = 2 ± √3

⇒ r = 2 + √3 {Since r > 1}