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.

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

If a^(x) = b^(y) = c^(z) and a, b, c, are in G.P., prove that x, y, z are in H.P.

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

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

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

If x^(1/a)=y^(1/b)=z^(1/c) where a,b,c are in A.P,,than show that x,y,z are in G.P.

If x, y, z are in A.P.; ax, by, cz are in GP. and 1/a, 1/b, 1/c are in A.P., then x/z+z/x is equal to

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 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.