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Math Help - Geometric Series

  1. #1
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    Geometric Series

    Hello, I've been trying to solve this problem: "How many generations must a person go back to have at least 1000 ancestors?"

    I've been trying ways to do it.. but not sure how. I know that the series goes like 2 + 4 + 8 and so on, so I know my a=2 and r=2. Don't really know where to go from there though. The question says at least 1000, so 1000 isn't a value I can plug into my equation.

    Not asking for anyone to solve, maybe just point me in the right direction on how to start. Thank you!
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  2. #2
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     S_n = \frac{a(1-r^n)}{1-r}

     1000 \geq \frac{2(1-2^n)}{1-2}

    solve for n.
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  3. #3
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    Quote Originally Posted by pickslides View Post
     S_n = \frac{a(1-r^n)}{1-r}

     1000 \geq \frac{2(1-2^n)}{1-2}

    solve for n.
    So I got this: 2^n \leq 501
    Is that right? I don't get how I find n.
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  4. #4
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    Given your arithmetic is correct then

     2^n \leq 501

     n \leq \log_2(501)

    or if you don't like/know logs you can use trial and error on n.
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