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Math Help - Closed form for a sequence

  1. #1
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    Closed form for a sequence

    i am having trouble with this sequence:

    x1=3 xn+1=0.8 xn-5 (n=1,2,3....)

    how do i find a closed form, also in the tenth term correct to 4SF

    Can someone explain how can i describe a long term behaviour of the sequence

    many thanks
    rich
    Last edited by mr fantastic; February 15th 2010 at 02:17 AM. Reason: Changed post title
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  2. #2
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    Quote Originally Posted by scouse280 View Post
    x1=3 xn+1=0.8 xn-5 (n=1,2,3....)
    Please use the math tag in order to make your equation readable. It is the third from right icon above the text editor and located next to the YouTube icon.

    Best,
    wirefree
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  3. #3
    MHF Contributor

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    Quote Originally Posted by scouse280 View Post
    i am having trouble with this sequence:

    x1=3 xn+1=0.8 xn-5 (n=1,2,3....)

    how do i find a closed form, also in the tenth term correct to 4SF

    Can someone explain how can i describe a long term behaviour of the sequence

    many thanks
    rich
    I take it that you mean x_1= 3 and x_{n+1}= 0.8x_n- 5. Notice that x_2= 0.8x_1- 5 and then x_3= 0.8(0.8x_1- 5)- 5= x_1(0.8)^2- 5(0.8)- 5, x_4= 0.8((0.8)^2x_1- 5(0.8)- 5)- 5= x_1(0.8)^3- 5(0.8)^2- 5(0.8)- 5
    Last edited by mr fantastic; February 15th 2010 at 02:18 AM. Reason: Fixed latex tags
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