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Thread: Geometric and arithmetic progression

  1. #1
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    Geometric and arithmetic progression

    a1, a2, a3 geometry progression

    24/a1 , 60/a2 , 126/a3 arithmetic

    the first 3 terms sum in geometric is 38 and the common ratio or quotient is less than 2
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  2. #2
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    Re: Geometric and arithmetic progression

    Quote Originally Posted by Mustafashama View Post
    a1, a2, a3 geometry progression
    24/a1 , 60/a2 , 126/a3 arithmetic
    the first 3 terms sum in geometric is 38 and the common ratio or quotient is less than 2
    $a_1=a,~a_2=a\cdot r,~\&~a_3=a\cdot r^2$ moreover $a+ar+ar^2=38$
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  3. #3
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    Re: Geometric and arithmetic progression

    You need a second equation to get a system of equations.

    $\dfrac{126}{ar^2}-\dfrac{60}{ar}=\dfrac{60}{ar}-\dfrac{24}{a}$

    Multiply out by $ar^2$ to get:
    $126-60r=60r-24r^2$

    $4r^2-20r+21=0$
    $(4r-7)(r-3)=0$
    Because the ratio is less than 2, this leaves only one solution. Plug that into the equation Plato showed you and solve for $a$.
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  4. #4
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    Re: Geometric and arithmetic progression

    Quote Originally Posted by SlipEternal View Post
    You need a second equation to get a system of equations.

    $\dfrac{126}{ar^2}-\dfrac{60}{ar}=\dfrac{60}{ar}-\dfrac{24}{a}$

    Multiply out by $ar^2$ to get:
    $126-60r=60r-24r^2$

    $4r^2-20r+21=0$
    $(4r-7)(r-3)=0$
    Because the ratio is less than 2, this leaves only one solution. Plug that into the equation Plato showed you and solve for $a$.
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