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JEE Main & Advanced Mathematics Sequence & Series Question Bank Harmonic Progression

  • question_answer
    Which number should be added to the numbers 13, 15, 19 so that the resulting numbers be the consecutive terms of a H.P.

    A) 7

    B) 6

    C) \[-6\]

    D) \[-7\]

    Correct Answer: D

    Solution :

    Suppose that \[x\] to be added then numbers 13, 15, 19 so that new numbers \[x+13,\ 15+x,\ 19+x\] will be in H.P. \[\Rightarrow \]\[(15+x)=\frac{2(x+13)(19+x)}{x+13+x+19}\] \[\Rightarrow \]\[{{x}^{2}}+31x+240={{x}^{2}}+32x+247\Rightarrow x=-7\] Trick: Such type of questions should be checked with the options.


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