A.P. and G.P.

Let a be the I term and d be the common difference of AP

So p^th  , q^th  ,r^th     , and s^th  terms of an A.P  will be a+(p-1)d , a+(q-1)d,a+(r-1)d ,a+(s-1)d

Now these terms are in GP so

a+(p-1)d /a+(q-1)d= a+(q-1)d/a+(r-1)d =a+(r-1)d /a+(s-1)d  = R

Applying compnendo and dividendo

R= (q-r)/(p-q)=(r-s)/(q-r) so (q-r)²=(r-s)(p-q) 

Therefore,(p-q) ,(q-r) ,(r-s) are  in G.P.