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If a, b, c are first three terms of a G.P. if the harmonic mean of a and b is 12 and arithmetic mean of b and c is 3 , then

Options

  1. Ano term of this G.P. is square of an integer
  2. Barithmetic mean of a, b, c is 3
  3. Cb= 6
  4. Dcommon ratio of this G.P. is 2

Correct answer

B. arithmetic mean of a, b, c is 3

Step-by-step solution

a, b, c are in GP 2 a b a+b =12, b+c 2 =3 2 a a r a+a r =12, a r+a r^2=6a r=6(1+r), ar (1+r)=6 i.e. 6(1+r)^2=6 , i.e. (1+r)^2=1 1+r= 1 i.e. r=0 or r=-2 r =-2 If r=-2 , then a=3 The GP is 3,-6,12,-24,48 Clearly no term of the series is square of an integer AM of a, b, c is = 3-6+12 3 =3

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