If p, q, r are in A.P.,  a is G.M. between p and q and  b is G.M between q and r, then a2,q2,b2  are in

Since p, q, r are in A.P.∴q=p+r2 ………………..(i)Since a is the G. M. between p, q∴a2=pq …………………(ii)Since b is the G. M. between q, r∴b2=qr ………………….(iii)From (ii) and (iii)p=a2q,r=b2q∴  (i) gives 2q=a2q+b2q⇒2q2=a2+b2⇒a2,q2,b2  are in A.P.