" (a) "[" If "(x+y)/(2),y,(y+z)/(2)" are in "HP," then "x,y,z" are in "],[," (b) GP "]

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

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

If x,y,z are in HP, then log(x+z)+log (x-2y+z) is equal to

(i) The value of x + y + z is 15. If a, x, y, z, b are in AP while the value of (1)/(x) + (1)/(y) + (1)/(z) " is " (5)/(3) . If a, x, y, z b are in HP, then find a and b (ii) If x,y,z are in HP, then show that log (x +z) + log (x +z -2y) = 2 log ( x -z) .

(i) The value of x + y + z is 15. If a, x, y, z, b are in AP while the value of (1)/(x) + (1)/(y) + (1)/(z) " is " (5)/(3) . If a, x, y, z b are in HP, then find a and b (ii) If x,y,z are in HP, then show that log (x +z) + log (x +z -2y) = 2 log ( x -z) .