If `x ,1,a n dz` are in A.P. and `x ,2,a n dz` are in G.P., then prove that `x ,a n d4,z` are in H.P.

If x,1,z are in A.P. and x,2,z are in G.P., then x,4,z are in

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

If x=Sigma_(n=0)^(oo) a^n,y=Sigma_(n=0)^(oo) b^n,z=Sigma_(n=0)^(oo) c^n where a, b,and c are in A.P and |a|lt 1 ,|b|lt 1 and |c|1 then prove that x,y and z are in H.P

If y-z,2(y-a),y-x are in H.P. prove that x-a,y-a,z-a are in G.P.

a,b,x are in A.P.,a,b,y are in G.P. and a,b,z are in H.P. then:

If x,1,z are in A.P. x,2,z are in G.P., show thast 1/x,1/4,1/z are in A.P.

If log, y, log, x, log, z are in G.P. xyz 64 and x y, z' are in A.P., then

If a,b,c are in G.P.,then prove that log a^(n),log b^(n),log c^(n)quad are in A.P.