# If the 2nd, 5th and 9th terms of a non-constant AP are in GP

If the 2nd, 5th and 9th terms of a non-constant A.P. are in G.P., then the common ratio of this G.P. is:

1. 4/3
2. 1
3. 7/4
4. 8/5

Solution

Let the terms of AP be A + d, A + 4d, A + 8d

Let the GP be a, ar, ar2

a = A + d

ar = A + 4d

ar2 = A + 8d

$$\dfrac{ar^2-ar}{ar-a} = \dfrac{(A+8d)-(A+4d)}{(A+4d)-(A+d)}= \dfrac{4}{3}$$

r = 4/3

The correct option is A.