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

2^nd , 5^th and 9^th terms of an A.P. are in G.P. 
$\Rightarrow a+d,a+4d,a+8d$ are in G.P.
$\Rightarrow {(a+4d)}^2=(a+d)(a+8d)$
$\Rightarrow a^2+16d^2+8ad=a^2+9ad+8d^2$
$\Rightarrow 8d^2=ad$
$\Rightarrow a=8d$
The term of G.P. are  $9d,12d,16d$
Common ratio $=\frac{12d}{9d}=\frac{4}{3}$