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Math Help - ordered pairs question

  1. #1
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    ordered pairs question

    if a b c are three natural numbers in Arithmetic progression and a+b+c=21 then all the possible values of the ordered triplet (a,b,c) is
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    If they are in arithmetric progression, a, b and c have a common difference, or:

    c - b = b - a = \dfrac{c - a}{2}

    Then;

    a + b + c = 21

    I think that should be okay to solve now.
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  3. #3
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    Quote Originally Posted by prasum View Post
    if a b c are three natural numbers in Arithmetic progression and a+b+c=21 then all the possible values of the ordered triplet (a,b,c) is
    Your AP is n,~n+d,~n+2d so n+n+d+n+2d=3n+3d=21.
    That means that n+d=7.
    The numbers of pairs that satisfy that depends on if we consider 0 a natural or not.

    Here is an example: n=3~\&~d=4 then the AP is 3,~7,~11.

    Can you finish?
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