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Sequence and series - Arithmetic mean question have been breaking my head

  1. Nov 7, 2011 #1
    1. The problem statement, all variables and given/known data
    Two consecutive numbers from 1,2,3.....n are removed A.M of remaining numbers is 105/4. Find n and those numbers removed .

    2. Relevant equations


    n = 50
    those numbers are 7 and 8

    3. The attempt at a solution

    I solved this question like a few weeks ago but now it escaped my brain I have no idea how .. and I am so annoyed now you know how it feels right?
    Ok so heres what I got
    The A.M of the total numbers would be
    n(n+1) / 2 / n

    that gives (n+1)/2

    now what we get after removing the numbers
    let the numbers be x and x+1
    therefore their sum = 2x+1

    now A.M after removing numbers

    n(n+1)/2 - (2x+1) / (n-2) = 105/4

    heres one I am not able to figyre out another relation PLease help somebody
  2. jcsd
  3. Nov 7, 2011 #2


    User Avatar
    Homework Helper

    Multiply both sides by 2(n-2).
    [tex]\frac{\frac{n(n+1)}{2} - (2x+1)}{n - 2} \cdot 2(n - 2) = \frac{105}{4} \cdot 2(n - 2)[/tex]
    Rearrange and you'll find yourself with a quadratic in n. Pretend for a moment that x is a constant, and solve for n using the quadratic formula. Then you'll need to guess-and-check some values of x to make the discriminant a perfect square.
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