If the pth, qth and rth terms of an A.P. be x,y,z repsectively, then show that : `x(q-r)+y(r-p)+z(p-q)=0`

If the pth , qth , rth , terms of a GP . Are x,y,z respectively prove that : x^(q-r).y^(r-p).z^(p-q)=1

The p^(th) , q^(th) and r^(th) terms of an A.P. are a, b, c, respectively. Show that (q -r)a+ (r-p )b + (p- q)c= 0

If pth, qth and rth terms of a HP be respectively a,b and c , has prove that (q-r)bc+(r-p)ca+(p-q)ab=0 .

Sum of first p,q and r terms of an A.P. are a,b,c respectively. Prove that a/p(q-r) +b/q(r-p) + c/r(p-q)=0 .

If the p^(th) , q^(th) and r^(th) terms of a G.P. are a, b and c, respectively. Prove that a^(q-r) b^(r-p)c^(P-q)=1 .

Sum of the first p, q and r terms of an A.P. are a, b and c, respectively. Prove that a/p(q-r)+b/q(r-p)+c/r(p-q)=0

If agt0,bgt0,cgt0 be respectively the pth, qth and rth terms of a G.P. are a, b ,c , prove that : (q-r) log a+ (r -p) log b + (p -q) log c = 0 .

If the 4th, 10th and 16th terms of a G.P. are x, y and z, respectively. Prove that x, y, z are in G.P.

If a,b,c are in A.P. and x,y,z are in G.P., then show that x^(b-c).y(c-a).z(a-b)=1 .

If p, q, r are in A.P. while x, y, z are in G.P., prove that x^(q-r).y^(r-p).z^(p-q) =1 .