Maths-
General
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Question

If a comma blank b comma blank c are in A.P., then fraction numerator a over denominator b c end fraction comma fraction numerator 1 over denominator c end fraction comma fraction numerator 2 over denominator b end fraction will be in

  1. A.P.   
  2. G.P.  
  3. H.P.   
  4. None of these  

The correct answer is: None of these


    a comma blank b, and c are in A.P. Hence,
    2 b equals a plus c (1)
    fraction numerator a over denominator b c end fraction plus fraction numerator 2 over denominator b end fraction equals fraction numerator a plus 2 c over denominator b c end fraction not equal to fraction numerator 2 over denominator c end fraction
    rightwards double arrow fraction numerator a over denominator b c end fraction comma fraction numerator 1 over denominator c end fraction comma fraction numerator 2 over denominator b end fraction are not in A.P.
    fraction numerator b c over denominator a end fraction plus fraction numerator b over denominator 2 end fraction equals fraction numerator 2 b c plus a b over denominator 2 a end fraction not equal to c
    Hence, the given numbers are not in H.P. Again,
    fraction numerator a over denominator b c end fraction fraction numerator 2 over denominator b end fraction equals fraction numerator 2 a over denominator b to the power of 2 end exponent c end fraction not equal to fraction numerator 1 over denominator c to the power of 2 end exponent end fraction
    Therefore, the given numbers are not in G.P.

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