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

  • question_answer
    If the \[{{7}^{th}}\] term of a H.P. is \[\frac{1}{10}\] and the \[{{12}^{th}}\] term is \[\frac{1}{25}\], then the \[{{20}^{th}}\] term is [MP PET 1997]

    A) \[\frac{1}{37}\]

    B)   \[\frac{1}{41}\]

    C)   \[\frac{1}{45}\]

    D)   \[\frac{1}{49}\]

    Correct Answer: D

    Solution :

    Considering corresponding A.P. \[a+6d=10\] and\[a+11d=25\]\[\Rightarrow \]\[d=3,\ a=-8\] \[\Rightarrow \]\[{{T}_{20}}=a+19d=-8+57=49\] Hence \[{{20}^{th}}\] term of the corresponding H.P. is \[\frac{1}{49}\].


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