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

  • question_answer
    The sixth H.M. between 3 and \[\frac{6}{13}\] is [RPET 1996]

    A)   \[\frac{63}{120}\]

    B)   \[\frac{63}{12}\]

    C)   \[\frac{126}{105}\]

    D)   \[\frac{120}{63}\]

    Correct Answer: A

    Solution :

    \[{{x}_{n}}=\frac{(n+1)ab}{na+b}\] Sixth H.M. \[{{x}_{6}}=\frac{7\ .\ 3\ .\ 6/13}{\left( 6\,.\ 3+\frac{6}{13} \right)}=\frac{126}{240}=\frac{63}{120}\].


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