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Infinity geometric series question

  1. Jun 14, 2006 #1
    Hi there everyone!
    Have a quick question for you.
    The question is:
    The sum to infinity of a geometric series is 9/2
    The second term of the series is -2
    Find the value of r, the common ratio of the series.

    I understand that we have to use the sum to infinity of a geometric series formula which is S(infinity) = a/1-r

    where a is the first term in the series and r is the common ratio.
    I also understand that s2 = s1*r.

    We're given the second term....but how do we get a? our first term?
    Any thoughts?
  2. jcsd
  3. Jun 14, 2006 #2

    matt grime

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    if you understand the second term is r times the first term, then you understand the first time is what times the second term?
  4. Jun 14, 2006 #3
    The first term is the second term over r.
    Well spotted!!
    I'll get the hang of this stuff yet!!
    Thanks very much
  5. Jun 14, 2006 #4


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    So you now know that a= -2/r and that
    [tex]\frac{a}{1-r}= \frac{-2}{r(1-r)}= 9/2[/tex]
    Solve for r.
    Last edited by a moderator: Jun 15, 2006
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