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If a, b, c are in AP ; b, c, d are in GP ; c, d , e are in HP, then which of the following is/are correct? 1. a, c and e are in GP 2. 1 a , 1 c , 1 e are in GP Select the correct answer using the code given below:

Options

  1. A1 only
  2. B2 only
  3. CBoth 1 and 2
  4. DNeither 1 nor 2

Correct answer

A. 1 only

Step-by-step solution

a, b, c are in AP 2 b=a+c ....(i) b, c, d are in GP c^2=b d ....(ii) c, d, e are in HP 2 d = 1 c + 1 e ....(iii) From (i) and (ii) aligned & 2 c^2=(a+c) d & 2 d = a+c c^2 & 1 c + 1 e = a c^2 + 1 c & 1 e = a c^2 c^2=a e aligned Hence, a, c, e are in GP.

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