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Math Help - Geometric Progression or Geometric Series

  1. #1
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    Geometric Progression or Geometric Series

    Find the total number of terms in the given geometric progression

    1, -3, 9,...., 531441

    Full procedure would be highly appreciated

    Please Help
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  2. #2
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    Quote Originally Posted by creatively12 View Post
    Find the total number of terms in the given geometric progression

    1, -3, 9,...., 531441

    Full procedure would be highly appreciated

    Please Help
    HI

    a=1 , r=-3 and the last term is 531441

    Using this formula ,

    T_n=ar^{n-1}

    where T_n = 531441 , r =-3 and a=1

    Solve for n .
    Last edited by mathaddict; October 8th 2009 at 07:15 AM.
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  3. #3
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    okay.... but I hav one question, how will you be able to find the power of -3, so that we would equate the bases and then equate their powers, is there a simple way other than LCM and Log to find the power ??
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  4. #4
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    Hello, creatively12!

    Find the number of terms in the geometric progression:
    . . 1,\;\text{-}3,\;9,\;\text{-}27,\; \hdots \;531,\!441

    The n^{th} term is: . a_n \:=\:a_1r^{n-1}
    . . where: . a_1 = first term, r = common ratio.

    We have: . a_1 = 1,\;r = \text{-}3

    Hence: . 1\cdot(\text{-}3)^{n-1} \:=\:531,\!441 \quad\Rightarrow\quad (\text{-}3)^{n-1} \:=\:531,\!441


    Since 3^{12} \:=\:531,\!441 \:=\:(\text{-}3)^{12}

    . . we have: . (\text{-}3)^{n-1} \:=\:(\text{-}3)^{12} \quad\Rightarrow\quad n-1 \:=\:12 \quad\Rightarrow\quad n \:=\:13


    There are 13 terms in the geometric progression.

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  5. #5
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    Quote Originally Posted by creatively12 View Post
    okay.... but I hav one question, how will you be able to find the power of -3, so that we would equate the bases and then equate their powers, is there a simple way other than LCM and Log to find the power ??
    Sorry , i made a mistake . Edited my post ..

    (-3)^{n-1}=531441

    you can see from the series that the positive terms are odd terms .

    So n must be odd , and (n-1) would be even .

    Since the power of -3 is even , then we can just ignore the -ve sign

    3^{n-1}=531441

    take the logs , then you would find that n=13 .
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  6. #6
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    really really thanks Soroban, but I still don't understand how to get that 3^12, that raise to the power 12 in an easy and simple way, but thanks for all the stuff
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  7. #7
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    thats what the problem, i don't know how to take logs, cause m not yet told to do logs
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  8. #8
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    Quote Originally Posted by creatively12 View Post
    thats what the problem, i don't know how to take logs, cause m not yet told to do logs
    ok

    531441 is  3^{12} which is also (-3)^{12}

    (-3)^{n-1}=(-3)^{12}

    By comparing the powers , n-1 =12 , n=13
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  9. #9
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    i just found out that my calculator does the trick of finding the powers, but thnaks anyways for the help, really appreciate it
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