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Math Help - Arithmetic series question

  1. #1
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    Arithmetic series question

    1. In an arithmetic series, three consecutive terms have a sum of -9 and a product of 48. Find the possible values of these terms.

    I really cant figure it out. I tries using the Sum of series formula and arithmetic series formula, but no results.
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  2. #2
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    Hello,
    Quote Originally Posted by milan View Post
    1. In an arithmetic series, three consecutive terms have a sum of -9 and a product of 48. Find the possible values of these terms.

    I really cant figure it out. I tries using the Sum of series formula and arithmetic series formula, but no results.
    Let k be the constant progression of the series.
    Let a,b,c the three consecutive terms.
    We have a+b+c=-9, abc=48
    But we also know that b=a+k and c=a+2k

    Does this help ?
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  3. #3
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    I know all that, but i dont know how to find the answer using it:P, thanx anyways though.
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  4. #4
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    Substituting b=a+k and c=a+2k in a+b+c=-9, you have :

    3a+3k=-9 \Rightarrow a+k=-3

    Now substituting in abc=48, you get :
    a(a+k)(a+2k)=48
    We know that a+k=-3.
    Hence -a(a+2k)=16 and furthermore, a=-3-k, so :
    -(-3-k)(-3-k+2k)=16
    (3+k)(-3+k)=16
    k^2-9=16

    So k=\pm 5

    If k=5, then a=-8 and b=\dots~,~c=\dots

    If k=-5, then ......................


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