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Thread: Genral Term

  1. #1
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    Genral Term

    Hi,

    Find the genral term of the G.P with third term 1 and the seventh term 8?

    Thanks!!!
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  2. #2
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    Geometric Series

    Btw, what does "genral" mean?
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  3. #3
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    The general term of any geometric sequence is given by

    Tn = $\displaystyle ar^{n-1}$

    where clearly, $\displaystyle a$ is the first term and $\displaystyle r$ is the common ratio of the geometric progression.


    So we have here,

    T3=1
    T7=8

    i.e. $\displaystyle ar^2=1$............(1)
    and$\displaystyle ar^6=8$............(2)

    Divide (2) by (1) to eliminate a
    so we have, $\displaystyle {r^6}/{r^2}$= 8/1

    so $\displaystyle r^4=8$
    $\displaystyle i.e. r = 8^{1/4}$

    $\displaystyle Now using the fact that ar^2=1$
    $\displaystyle we have, a(8)^{1/2}=1$

    $\displaystyle so a = 8^{-1/2}$

    $\displaystyle Hence the general term of the series is given by$
    $\displaystyle Tn= 8^{-1/2}(8^{1/4})^{n-1}$
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  4. #4
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    Mr Banded Krait, I would like to see a space between your words
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  5. #5
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    Quote Originally Posted by Wilmer View Post
    Mr Banded Krait, I would like to see a space between your words
    [tex]\text{Hence the general term of the series is given by}[/tex] gives $\displaystyle \text{Hence the general term of the series is given by}$
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