If a,b,c, be the pth,qth nd rth terms respectively of a Geometric progression, and a,b,cgt0 then show that: `(q-r)loga+(r-p)logb+(p-q)logc=0`

(iii) If a,bc are respectively the pth,qth and rth terms of the given G.P. then show that (q-r)log a+(r-p)log b+(p-q)log c=0, where a,b,c>0.

If a,b,c are respectively the p^(th), q^(th) and r^(th) terms of the given G.P. then show that (q - r) log a + (r - p) log + (p - q) log c = 0, where a, b, c gt 0

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, and c are respectively,the pth,qth, and rth terms of a G.P.,show that (q-r)log a+(r-p)log b+(p-q)log c=0

If a, b, c be the pth, qth and rth terms respectively of a HP, show that the points (bc, p), (ca, q) and (ab, r) are collinear.

If a,b,c are respectively the p^(th),q^(th) and r^(th) terms of a G.P.show that (q-r)log a+(r-p)log b+(p-q)log c=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

If a,b,c are the pth,qth,rth terms, respectively,of an HP,show that the points (bc,p),(ca,q), and (ab,r) are collinear.