Three positive numbers form an increasing GP

• Sequences Series

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

1. √2 + √3
2. 2 + √3
3. 2 - √3
4. 3 + √2

Answer

Let numbers be a, ar, ar²

Now, 2(2ar) = a + ar²,  [a ≠ 0]

4r = 1 + r²

r² - 4r + 1 = 0

The correct option is B.