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If (a+b), 2 b,(b+c) are in HP, then which one of the following is correct?

Options

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

Correct answer

C. a , b and c are in GP

Step-by-step solution

since, a+b, 2 b, b+c are in H.P 1 a+b , 1 2 b , 1 b+c are in A.P 2 a+b , 1 b , 2 b+c are in A.P 1 b - 2 a+b = 2 b+c - 1 b 1 b = a+2 b+c (a+b)(b+c) ab + ac + b ^2+ bc = ab +2 ~b ^2+ bc b ^2= ac a , b , c are in G.P.

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