Three positive numbers form an increasing G . P . If the middle term in this G . P . is doubled, the new numbers are in A . P . Then the common ratio of the G . P . is :

Step-by-step solution

Let the three numbers of the GP be a ,   a r and a r 2 where r is the common ratio. According to the given condition, a ,   2 a r and a r 2 are in AP. ∴    2 a r = a + a r 2 2 ∴    a + a r 2 = 4 a r ∴    r 2 + 1 = 4 r ∴    r 2 - 4 r + 1 = 0 ∴   r = 4 ± 1 6 - 4 2 = 4 ± 2 3 2 = 2 ± 3 As it is an 'increasing' GP, r   >   1 . ∴   r = 2 + 3 .