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Linear second-order recurrence sequences

  1. Jan 15, 2008 #1
    Hello,

    I hope I have posted this in the correct place, if not, sorry.

    Okay, I have just started working through the material, but I am having some problems working out one of the examples, which is given below:

    Un+2 = 12Un+1 - 20Un (n = 0,1,2...)

    We are given
    U0 = 1, U1 = 2

    and are asked to work out U2 to U4.

    But, maybe my head is just blocked, but I can't seem to get the figures. I have looked at the answers at the back of the book, but still no luck.

    So, if anyone could point me in the right direction, I would be very thankful.

    Cheers
    Sean

    PS - Sorry about typing the question out, I haven't got the hang of LaTeX just yet.
     
  2. jcsd
  3. Jan 15, 2008 #2
    When n is 0, the line
    [tex]U_{n+2} = 12 U_{n+1} - 20 U_n[/tex]​
    becomes
    [tex]U_2 = 12 U_1 - 20 U_0[/tex]​
    n values of 1, 2, 3, ... will give you further terms of the sequence.

    P.S.: You can click on the equations in this post, to see the corresponding LaTex for them.
     
  4. Mar 14, 2008 #3
    Please go another step forward

    What I would like to know is when n=1, and when n=2? What are the substitutions there then?
     
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