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How many terms of the AP …

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How many terms of the AP 26,21,16,11,.... are needed to give the sum 11?

    • Posted by Lucifer?? Morningstar?? 5 years, 6 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Gaurav Seth 5 years, 6 months ago

    'a' or the first term=26
    and 'd' or the common difference =21-26=-5
    n=?
    Sum of n terms of A.P=11
    Sum of n terms of A.P=n/2(2a+(n-1)d
    11=n/2(52-5n+5)
    22=n(57-5n)
    22=57n-5n2
    5n2-57n+22=0
    By splitting the middle term,
    5n2-55n-2n+22=0
    5n(n-11)-2(n-11)=0
    (5n-2)(n-11)=0
    n-11=0
    n=11

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