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If 2^ 1 c , 2^ b a c , 2^ 1 a are in GP, then which one of the following is correct?

Options

  1. Aa, b, c are in AP
  2. Ba, b, c are in GP
  3. Ca, b, c are in HP
  4. Da b, b c, c a are in AP

Correct answer

A. a, b, c are in AP

Step-by-step solution

2^ 1 c , 2^ b a c , 2^ 1 a are in GP (2^ b a c )^2=2^ 1 c 2^ 1 a 2^ 2 b a c =2^ 1 c + 1 a 2 b a c = 1 c + 1 a = a+c a c 2 b=a+c a, b, c are in AP.

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