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Math Help - 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 = ar^{n-1}

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


    So we have here,

    T3=1
    T7=8

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

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

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

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

    so  a = 8^{-1/2}

    Hence  the  general  term  of  the  series  is  given  by
    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 \text{Hence  the  general  term  of  the  series  is  given  by}
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