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If x, 3 2 , z are in AP; x, 3, z are in GP; then which one of the following will be in HP?

Options

  1. Ax, 6, z
  2. Bx, 4, z
  3. Cx, 2, z
  4. Dx, 1, z

Correct answer

A. x, 6, z

Step-by-step solution

x , 3 2 , z are in A.P If a, b, c are in A.P 2 b=a+c aligned & 2 ( 3 2 )= x + z & 3= x + z ...(1) & x , 3, z are in G.P. aligned If a, b, c are in G.P. b^2= ac aligned & 3^2= xz & 9= xz ...(2) aligned If x, 6, z are in H.P. 2 6 = 1 x + 1 z aligned & ( 2 b = 1 a + 1 c , if a, b, c are is H.P. ) & 1 3 = z+x x z = 3 9 = 1 3 ( from (1)(2)) & L.H.S. = R.H.S. aligned

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