The $2^{nd}$, $4^{th}$ and $9^{th}$ terms of an AP The $2^{nd}$, $4^{th}$ and $9^{th}$ terms of an arithmetic progression are in geometric progression. Calculate the common ratio of the geometric progression.
My Attempt:
For A.P
$$T_2=a+d$$
$$T_4=a+3d$$
$$T_9=a+8d$$
Now, 
$$a+d, a+3d, a+8d$$
are in GP.
So,
$$\frac {a+3d}{a+d}=\frac {a+8d}{a+3d}$$.
Now, How should I solve further.?


How should I solve further?

Assume $d \ne 0$, otherwise the sequence is constant. 
Now divide each numerator and denominator of your last equation by $d$ to  get
$$\frac {\frac{a}{d}+3}{\frac{a}{d}+1}=\frac {\frac{a}{d}+8}{\frac{a}{d}+3}$$
and substitate $\frac{a}{d}$ by $r$:
$$\frac {r+3}{r+1}=\frac {r+8}{r+3}$$
This gives $r=\frac{1}{3}$.
So we have 
$$\frac{T_4}{T_2}=\frac {a+3d}{a+d}=\frac {\frac{a}{d}+3}{\frac{a}{d}+1}=\frac {r+3}{r+1}=\frac {\frac{1}{3}+3}{\frac{1}{3}+1}=\frac{5}{2}$$
