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

  • question_answer
    If \[{{5}^{th}}\] term of a H.P. is \[\frac{1}{45}\]and \[{{11}^{th}}\] term is \[\frac{1}{69}\], then its \[{{16}^{th}}\]  term will be [RPET 1987,  97]

    A) 1/89

    B) 1/85

    C) 1/80

    D) 1/79

    Correct Answer: A

    Solution :

    Here \[{{5}^{th}}\] term of the corresponding A.P. \[=a+4d=45\] ?..(i) and \[{{11}^{th}}\] term of the corresponding A.P.\[=a+10d=69\] ?..(ii) From (i) and (ii), we get  \[a=29,\ d=4\] Therefore \[{{16}^{th}}\] term of the corresponding A.P. =\[a+15d=29+15\times 4=89\]. Hence \[{{16}^{th}}\] term of the H.P. is \[\frac{1}{89}\].


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