Given that  three numbers from an increasing GP

Let the 3 number are: a, ar, ar² (r > 1)

Now, according to question,

a, 2ar, ar²  are in AP

So, 2ar - a = ar² - 2ar

=> a(2r - 1) = a(r² - 2r)

=> 2r - 1 = r² - 2r

=> r² - 2r - 2r + 1 = 0

=> r² - 4r + 1 = 0

=> r = [4 ± √{16 - 4*1*1}]/2

=> r = [4 ± √{16 - 4}]/2

=> r = {4 ± √12}/2

=> r = {4 ± 2√3}/2

=> r = {2 ± √3}

Since r > 1

So, the common ratio of the GP is (2 + √3)