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Math Help - Geometric Series

  1. #1
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    Geometric Series

    I have a problem with finding the sum of this geometric series. (the characters in italics are supposed to be smaller)

    a1 = 2, a6 = 486, r = 3

    So, applying the sum formula:

    Sn = a1 (1 - r^n) / 1 - r

    Sn = 2 (1 - 3^n) / 1 - r

    I don't have n to figure it out with this formula, instead I have a6, the 6th term. What am I supposed to do with that?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by BlueStar View Post
    I have a problem with finding the sum of this geometric series. (the characters in italics are supposed to be smaller)

    a1 = 2, a6 = 486, r = 3

    So, applying the sum formula:

    Sn = a1 (1 - r^n) / 1 - r

    Sn = 2 (1 - 3^n) / 1 - r

    I don't have n to figure it out with this formula, instead I have a6, the 6th term. What am I supposed to do with that?
    what sum did they ask you to find? the sum of the first what terms? six? if so, n = 5, if you start your series counting from zero, which in this case, i think is what you did

    the terms of a geometric series are given by: \sum_{n = 1}^{ \infty} a_1 r^{n - 1} or \sum_{n = 0}^{ \infty} a_1 r^{n}
    Last edited by Jhevon; July 14th 2007 at 01:51 PM.
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  3. #3
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    Hello, BlueStar!

    Is that the original wording of the problem? . . . It is truly strange.
    . . There is too much information.

    If the first term is: a_1 = 2 and the common ratio is: r = 3
    . . we can use: . a_n = a_1r^{n-1} and find that: . a_6 \:=\:2\!\cdot\!3^5 \:=\:486

    If the first term is: a_1 = 2 and the sixth term is: a_6 = 486
    . . then: . 486 \:=\:2\!\cdot r^5\quad\Rightarrow\quad r = 3

    If the sixth term is: a_6 = 486 and the common ratio is: r = 3
    . . then: . 486 \:=\:a_1\!\cdot\!3^5\quad\Rightarrow\quad a_1 = 2

    That is, with two of the facts, we can determine the third.
    . . So why gives redundant statements?

    On the other hand, they didn't tell us how many terms are in the series.
    . . Did I say "strange"? .I meant silly.

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