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Pascals Triangle, arithmetic sequence.

  1. Feb 25, 2012 #1
    1. The problem statement, all variables and given/known data

    Write down the condition for the numbers p, q, r to form an arithmetic sequence.


    2. Relevant equations



    3. The attempt at a solution

    Have no idea, but I looked at the answer and they have assigned each letter with a given value (number). How is this possible?
     
  2. jcsd
  3. Feb 25, 2012 #2
    sorry the answer is q = 1/2 (p + r)

    then they ask for it in a geometric sequence, and the answer to this q^2 = pr

    any help would be appreciated... I tried searching the net but they only had examples with numbers containing a certain distance between each other. ie 5,7,9,11....
     
  4. Feb 25, 2012 #3
    Hi sg001
    An arithmetic sequence means for p, q, r that to get q from p, you add a constant.
    and to get r from q, you add the same constant.
    If you look at p, q, r, (say, put them on a ruler for instance) you will see that q is necessarily in the middle of p and r (since they are separated appart by the same constant).
    This is what this answer says.
    For a geometric sequence, the same observation holds, except on a logarithmic scale, if you look at the answer and take the logarithm, you will see this is exactly the same formula.

    Cheers...
     
  5. Feb 25, 2012 #4
    Thanks for the help I think I get it now!
     
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