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

Options

A. `(8)/(5)`
B. `(4)/(3)`
C. 1
D. `(7)/(4)`

Answer

B

Explanation

Let a be the first term and d be the common difference of the A.P. It is given that
`a_(2)=a+d,a_(5)=a+4danda_(9)=a+8d` are in G.P.
`:." "a_(5)^(2)=a_(2)xxa_(9)`
`rArr" "(a+4d)^(2)=(a+d)(a+8d)`
`rArr" "a=8d`
`:." "a_(2)=9d,a_(5)=12d,a_(9)=16d`
The common ratio of the G.P. `(a_(5))/(a_(2))=(12d)/(9d)=(4)/(3)`.