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Math Help - Geometric series

  1. #1
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    Geometric series

    A geometric series has first term a and common ratio r where r\geqslant 1
    The sum of the first four terms of this series is 15 times the first term.

    a) show that r^3 + r^2 +r -14=0

    and having S4 = 15a
    I've done the first part
    But I don't get b
    b) Show that r=2 is the only real solution for this equation.


    Every time I use Latex I get an error when I preview, has anything changed?
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  2. #2
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    The previous LaTeX routine, that used "math" and "/math" isn't working. However, it appears that using "tex" and "\tex" will work:
    r^3+ r^2+ r- 14= 0

    To show that "r= 2 is the only real solution for this equation", first show that r= 2 is a solution:
    2^3+ 2^2+ 2- 14= 8+ 4+ 2- 14= 0

    And since r= 1 is soluton, x- 2 is a factor of that equation:
    r^3+ r^2+ r- 14= (x- 2)(ax^2+ bx+ c)

    What you need to do is find that quadratic factor- find a, b, c by, perhaps by multiplying out the right side and setting corresponding cooefficients equal, getting three equations for a, b, and c, perhaps by dividing r^3+ r^2+ r- 14 by x- 2- and showing that the quadratic has no real zeros.
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  3. #3
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    Quote Originally Posted by elieh View Post
    A geometric series has first term a and common ratio r where r\geqslant 1
    The sum of the first four terms of this series is 15 times the first term.
    a) show that r^3 + r^2 +r -14=0 and having S4 = 15a
    I've done the first part
    But I don't get b
    b) Show that r=2 is the only real solution for this equation.
    Use the [tex] tags [tex](2)^2+(2)^2+(2)-14=0[/tex] gives (2)^2+(2)^2+(2)-14=0.

    Note that r^3+r^2+r-14=(r-2)(r^2+3r+7)
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  4. #4
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    Makes sense,
    Thanks guys.
    Test:
    x^2
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