Question

Three numbers form an increasing G. P. If the middle term is doubled , then the new numbers are in A. P. Find the common ratio of the G. P.

Answer 1

Hi, let the numbers be a, ar, ar^2 (r>1)
According to question, 
a, 2ar, ar^2 are in A.P.
b-a=c-b
2b=a+c
Now! 2(2ar)=a+ar^2  (a not equal to 0)

4r=1+r^2
r^2-4r+1=0
          Applying Quadratic equation! -b+/-√b^2-4ac÷2a
r=2+/-root of 3
r=2+root of 3    (+ only)

If you have any doubts, plz post it below. :)

Answer 2

Answer:

(a) 2 + √3

Step-by-step 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)