If `p ,q ,a n dr` are inA.P., show that the pth, qth, and rth terms of any G.P. are in G.P.

If p,q,r are in A.P.show that the pth,qth and rth terms of any G.P.are in G.P.

If p,q,r are in AP then prove that pth,qth and rth terms of any GP are in GP.

If p ,q ,a n dr are in A.P., then which of the following is/are true? pth, qth, and rth terms of A.P. are in A.P. pth, qth, rth terms of G.P. are in G.P. pth, qth, rth terms of H.P., are in H.P. none of these

If x ,y ,a n dz are pth, qth, and rth terms, respectively, of an A.P. nd also of a G.P., then x^(y-z)y^(z-x)z^(x-y) is equal to a.x y z b. 0 c. 1 d. none of these

Suppose a, b, c gt 0 and are respectively the pth, qth and rth terms of a G.P. Let x=(loga)i+(logb)j+(logc)k y=(q-r)i+(r-p)j+(p-q)k If angle between x and y is kpi , then k = ______

If a,b,and c are positive and are the pth, qth and rth terms respectively of a GP. Show without expanding that |{:(loga,p,1),(logb,q,1),(logc,r,1):}|=0

If a,b,c are positive and are the pth, qth and rth terms respectively of a G.P., the the value of |(loga, p, 1),(logb, q, 1),(logc, r, 1)|= (A) 1 (B) pqr(loga+logb+logc) (C) 0 (D) a^pb^qc^r