If `a^x=b^y=c^z `and a,b,c are in G.P. show that `1/x,1/y,1/z` are in A.P.

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.

Which of the foliowing statement(s) is/are true? (A) If a^x =b^y=c^z and a,b,c are in GP, then x, y, z are in HP (B) If a^(1/x)=b^(1/y)=c^(1/z) and a,b,c are in GP, then x,y,z are in AP

Let a(a!=0) is a fixed real number and (a-x)/(px)=(a-y)/(qy)=(a-z)/(rz). If p,q,r are in A.P.show that (1)/(x),(1)/(y),(1)/(z) are in A.P.

If a,b,c,d be in G.P. and a^x=b^y=c^z=d^w , prove that 1/x,1/y,1/z,1/w are in A.P.

If reciprocals of (x+y)/2,y, (y+z)/2 are in A.P., show that x,y,z are in G.P.

IF a,b,c are in G.P and a^(1/x)=b^(1/y)=c^(1/z) then x,y,z are in