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

If a,b,c, d are in G.P., show that : a+b,b+ c and c+d are also in G.P.

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 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

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 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 (m+1)t h ,(n+1)t h ,a n d(r+1)t h terms of an A.P., are in G.P. and m ,n ,r are in H.P., then find the value of the ratio of the common difference to the first term of the A.P.

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 G.P. are p, q and x, respectively. Show that q^2=ps .

The pth, (2p)th and (4p)th terms of an AP, are in GP, then find the common ratio of GP.

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 .