If the pth, qth and rth terms of an A.P. are in G.P., then the common ratio of the G.P. is

pth, qth, rth terms of A.P. area+(p−1)d=x………..(i)a+(q−1)d=xR……..(ii)a+(r−1)d=xR2…….(iii)where R is common ratio of G.P.Subtracting (2) from (3) and (1) from (2) and then dividingthe former by the later, we haveq−rp−q=xR2−xRxR−x=R