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Math Help - Geometric Sequences and Series

  1. #1
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    Geometric Sequences and Series

    Q. If Un of the sequence 2, 4, 8,... is 512, find n.

    Eq.: Un = ar^n-1

    Attempt:
    Un = ar^n-1
    2.2^n-1 = 512
    n = 9

    My question is, can n be solved without randomly subbing values into n? Thank you.
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  2. #2
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    Re: Geometric Sequences and Series

    you can use logarithms
    Last edited by waqarhaider; July 25th 2011 at 04:06 AM.
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  3. #3
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    Re: Geometric Sequences and Series

    Quote Originally Posted by GrigOrig99 View Post
    Q. If Un of the sequence 2, 4, 8,... is 512, find n.

    Eq.: Un = ar^n-1

    Attempt:
    Un = ar^n-1
    2.2^n-1 = 512
    n = 9

    My question is, can n be solved without randomly subbing values into n? Thank you.
    the author of these "formulated" problems expects that the student knows

    512 = 2^9
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    Re: Geometric Sequences and Series

    Quote Originally Posted by waqarhaider View Post
    [Tex]\mbox{you\can\use\logarithms[\Tex]
    I don't think GrigOrig99 has already learned logarithms.
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    Re: Geometric Sequences and Series

    Quote Originally Posted by GrigOrig99 View Post
    Q. If Un of the sequence 2, 4, 8,... is 512, find n.

    Eq.: Un = ar^n-1

    Attempt:
    Un = ar^n-1
    2.2^n-1 = 512
    n = 9

    My question is, can n be solved without randomly subbing values into n? Thank you.
    u_1=2=2^1

    u_2=4=2^2

    u_3=8=2^3

    u_n=2^n

    If you wish, you may keep doubling until you reach 512

    u_4=16,\;\;\;u_5=32,\;\;\;u_6=64....\;\;etc
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    Re: Geometric Sequences and Series

    Apologies if I was unclear. I understand why n = 9, i.e. 2^9 = 512. What I meant was whether or not 9, itself, can be calculated from just:

    2.2^n-1 = 512

    I don't believe it's possible but just wanted to double check with you guys. Thanks again.
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  7. #7
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    Re: Geometric Sequences and Series

    You may use the Power Law of logarithms.

    2^n=512\Rightarrow\ log2^n=log512

    Now use

    loga^b=bloga

    nlog2=log512

    n=\frac{log512}{log2}

    Natural logs or "logs to base 10" may be used.
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  8. #8
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    Re: Geometric Sequences and Series

    Thank you for clearing that up. I'm getting better at doing most of these sums on my own, slowly but surely.
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  9. #9
    MHF Contributor Siron's Avatar
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    Re: Geometric Sequences and Series

    Sorry, then I've to take back what I said about that you haven't learnt logarithms yet .
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