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Math Help - Common ratio problems

  1. #1
    Junior Member
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    Exclamation Common ratio problems

    Been having problems with the solutions to the following problems dealing with finding the common ratio.

    Solve for the missing variable and find the common ratio
    1.) <br />
\sqrt{x},3,3\sqrt{x}<br />

    2.) <br />
m+2,m+4,2m+11<br />
    Last edited by nightrider456; March 2nd 2010 at 05:36 PM.
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  2. #2
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    Hello, nightrider456!

    If we are given three terms a,b,c with a common ratio,

    . . then: . \frac{a}{b} \:=\:\frac{b}{c}


    Solve for the variable and find the common ratio.

    . . (1)\;\;\sqrt{x},\;3,\;3\sqrt{x}

    We have: . \frac{\sqrt{x}}{3} \;=\;\frac{3}{3\sqrt{x}} \quad\Rightarrow\quad 3x \:=\:9 \quad\Rightarrow\quad x \:=\:3

    The three terms are: . \sqrt{3},\;3,\;3\sqrt{3}

    . . The common ratio is: . \sqrt{3}




    (2)\;\;m+2,\;m+4,\;2m+11

    We have: . \frac{m+2}{m+4} \:=\:\frac{m+4}{2m+11} \quad\Rightarrow\quad 2m^2 + 15m + 22 \:=\:m^2 + 8m + 16

    . . m^2 + 7m + 6 \:=\:0 \quad\Rightarrow\quad (m+1)(m+6) \:=\:0

    Hence: . m \;=\;-1,\:-6 . . . two solutions


    If m = -1, the three terms are: . 1,\:3,\:9
    . . The common ratio is: . 3


    If m = -6, the three terms are: . -4,\:-2,\:-1
    . . The common ratio is: . \tfrac{1}{2}

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