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Rajan@2021
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The sum of the first 7 terms of an AP is 182. If its 4th and 17th terms are in the ratio 1:5, find the AP.

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An important and exam oriented question from arithmetic progression chapter in which we are to find the AP, if the sum of the first 7 terms of an AP is 182 and its 4th and 17th terms are in the ratio 1:5.

Book RS Aggarwal, Class 10, chapter 5C, question no 27.

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1 Answer

  1. S7=7/2[2a+(71)d]=182

    182=7/2[2a+6d]……..(1)

    an=a+(n1)d

    a4=a+(41)d=a+3d

    a17=a+(171)d=a+16d

    From given, we have,

    a4​/a17=(a+3d)/(a+16d)

    1/5=(a+3d)/(a+16d)

    5a+15d=a+16d

    solving the above equation, we get,

    4a=d

    using this value in (1), we get,

    182=7/2[2a+6(4a)]

    solving the above equation, we get,
    a=2
    4(2)=8=d

    The series as follows,

    a,a+d,a+2d,.........
    2,10,18,.......

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