If the pth,qth,rth terms of an AP are in GP prove that the common ratio of the GP is. q-r/p-q

Let first term of the AP = a and common difference = d 
pth of an AP= a+(p−1)d 
qth of an AP= a+(q−1)d 
rth of an AP= a+(r−1)d 
are in G.P 
Let first term of the GP be x and common ratio be y 
then 
a+(p−1)d=x........(i) 
a+(q−1)d =xy........(ii) 
a+(r−1)d=xy² ........(iii) 
Subtract (i) from (ii) and get 
(q−1)d −(p−1)d=xy−x 
→(q−p)d=xy−x......(iv) 
Subtract (ii) from (iii) and get 
(p−1)d −(r−1)d=xy²−xy =y(xy−x) 
→(q−r)d=y(xy−x) .....(v) 
divide (v) by (iv) and get 
(q−r)/(p−q)= y