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Math Help - linear recureence sequences

  1. #1
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    linear recureence sequences

    (c) Consider the linear recurrence sequence
    x
    1 =23,xn+1 =1.3xn 12
    (
    n =1,2,3,...).
    (i)
    Find a closed form for the sequence.
    [
    4]
    (ii) Use the closed form to find the eighth term of the sequence,
    correct to four significant figures.
    [
    1]
    (iii) Describe the long-term behaviour of the sequence.
    [
    2]
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  2. #2
    Senior Member vincisonfire's Avatar
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    You should find that
     x_o=\frac{35}{1.3}
     x_1=1.3 \cdot x_o - 12
     x_2=1.3 \cdot (1.3 \cdot x_o - 12) -12 = 1.3^2 \cdot x_o - (1.3 + 1 ) \cdot 12
     x_3=1.3^3 \cdot x_o - (1.3^2 + 1.3 + 1 ) \cdot 12
     x_n=1.3^n \cdot x_o - (1.3^{n-1} + 1.3^{n-2} + ... + 1.3 +1 ) \cdot 12
    You alright for number two and I guess that by computing some value you can do number 3 alone.
    Last edited by vincisonfire; October 20th 2008 at 07:43 AM.
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