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Math Help - Geometric Sequences

  1. #1
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    Geometric Sequences

    I'm having a little trouble understanding this stuff. Sequences in general, really, but I've chosen a geometric one to list here.

    It's a rather simple question but I can't seem to find anything that answers it.

    Determine the number of terms:

    4, 12, 36, ... , 972
    Now, I've tried this problem and this is what I did.
    Tn = ar^n-1
    = 972 = 4(3)^n-1
    = 243 = 3^n-1. [243 = 3^5]
    Therefore 3^n - 1 = 3^5

    There are five numbers in the term.


    That's what I've done, yet my textbook tells me that the answer is actually six. I have no idea how they got that and I'm beginning to suspect a typo. Any help?

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  2. #2
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    wow... that makes me feel dumb. Ha ha. Well thank you very much. I guess I've been looking at sequences too long.
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  3. #3
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Aerillious View Post
    wow... that makes me feel dumb. Ha ha. Well thank you very much. I guess I've been looking at sequences too long.
    Don't worry. I made the same mistake not too long ago. That's how I recognized it so quickly.

    -Dan

    Edit: Ah well. "Against stupidity the gods themselves contend in vain."
    Last edited by topsquark; October 9th 2007 at 03:29 PM.
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    the problem is you should have equated n - 1 = 5 ---> n = 6

    as the formula is written here, we start with n = 1, not 0.



    Geometric sequence:

    a_n = ar^n for n = 0,1,2,3,4... .........here, (n + 1) gives the number of the term

    or

    a_n = ar^{n - 1} for n = 1,2,3,4... ................here, n gives the number of the term



    you used the last formula, so starting at n = 1 was correct, the problem is you solved the first equation i mentioned incorrectly.
    Last edited by Jhevon; October 9th 2007 at 03:42 PM.
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  5. #5
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    That makes a lot of sense, actually. Thank you. I think I need to get the hang of the difference between positive and negative sequences...

    I'm really close to understanding it all, it's just a little elusive.
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