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Thread: 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 $\displaystyle a,b,c$ the three consecutive terms.
    We have $\displaystyle a+b+c=-9$, $\displaystyle abc=48$
    But we also know that $\displaystyle b=a+k$ and $\displaystyle c=a+2k$

    Does this help ?
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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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    Substituting $\displaystyle b=a+k$ and $\displaystyle c=a+2k$ in $\displaystyle a+b+c=-9$, you have :

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

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

    So $\displaystyle k=\pm 5$

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

    If $\displaystyle k=-5$, then ......................


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