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

$a+d,a+4d,a+8d$ are in G.P.

$\begin{array}{l}\Rightarrow {\left(a+4d\right)}^2=\left(a+d\right)\left(a+8d\right)\\ \Rightarrow a^2+16d^2+8da=a^2+9ad+8d^2\\ \Rightarrow 8d^2-ad=0\\ \Rightarrow d(8d-a)=0\\ \Rightarrow a=8d\\ \therefore r=\frac{a+4d}{a+d}=\frac{12d}{9d}=\frac{4}{3}\end{array}$