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Math Help - Another geometric series

  1. #1
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    Another geometric series

    Please help...

    the sum of the first n terms of a positive geomtetric sequence is 315 and the sum of the 5th 6th and 7th term is 80640. identify the sequence.

    I have no idea how to find a, or r. thanks xxx
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  2. #2
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    Sn=a(1-r^n)
    ------1-r
    Un= ar^(n-1) (i think off the top of my head)

    315=a(1-r^n)
    -------1-r

    5th term:
    U5=ar^4
    U6=ar^5
    U7=ar^6
    so

    80640=ar^4 + ar^5 + ar^6

    80640=ar^4(1-r^3)
    ----------1-r
    Hopefully by solving the simultaneous equation you can get a and r, then go back to your original equation (with 315) to find n
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  3. #3
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    Hello, mathshelpneeded!

    There must be a typo . . .
    As stated, there is no unique solution.
    . . There are three variables and only two equations.

    I believe that the "n" is a "3" . . .


    The sum of the first 3 terms of a positive geometric sequence is 315
    and the sum of the 5th, 6th and 7th term is 80,640.
    Identify the sequence.

    The sum of the first 3 terms is: .a + ar + arē .= .315

    The sum of the 5th, 6th and 7th terms is: .ar^4 + ar^5 + ar^6 .= .80,640


    . . Factor the first equation: .a(1 + r + rē) .= .315 .[1]

    Factor the second equation: .ar^4(1 + r + rē) .= .80,640 .[2]

    . . . . . . . . . . . . . .ar^4(1 + r + rē) . . .80,640
    Divide [2] by [1]: . ------------------- .= .--------
    . . . . . . . . . . . . . . .a(1 + r + rē) . . . . . 315

    . . And we have: .r^4 = 256 . . r = 4


    Substitute into [1]: .a(1 + 4 + 4ē) .= .315 . . a = 15


    The sequence is: .15, 60, 240, 960, 3,840, 15,360, 61,440, ...

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