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`.

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

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 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.

The 5th, 8th and 11th terms of a G.P. are p, q and x, respectively. Show that q^2=ps .

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 .

The 4th, 7th and 10th terms of a GP. are a, b, c respectively. Show that b^2 = ac .

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

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 .

The 5th, 8th, and 11th terms of a GP are p, q and s respectively. Find relation between p,q and s.

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 .