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 that 1/x,1/4,1/z are in A.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)/(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 (b+c)/a,(c+a)/b,(a+b)/c are in A.P. show that 1/a,1/b1/c are also in A.P. (a +b+c != 0) .

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^x=b^y=c^z and b^2=a c , then show that y=(2z x)/(z+x)

If a, b, c are in A.P., b, c, d are in G.P. and 1/c ,1/d ,1/e are in A.P. prove that a, c, e are in G.P.

If a, b, c are in A.P., b, c, d are in G.P. and 1/c ,1/d ,1/e are in A.P. prove that a, c, e are in G.P.

If a, b, c are in A.P., b, c, d are in G.P. and 1/c ,""1/d ,""1/e are in A.P. prove that a, c, e are in G.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.