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Homework Help: Recursive function

  1. Oct 2, 2009 #1
    1. The problem statement, all variables and given/known data

    Solve the recursive function:

    A_{n+1} = (8/9)A_{n} + (24/9)*(20/9)^n

    We want a closed formula for A_n

    2. Relevant equations

    I'm just doing this to work out the surface area of the Menger Sponge.

    I know the formula's probably out there, but I get this recursive formula and I don't know how to solve it.

    3. The attempt at a solution

    I tried getting it in terms of A_{0}, which is 6, but I couldn't seem to simplify it... please help?!
  2. jcsd
  3. Oct 2, 2009 #2


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    Gold Member

    First solve the homogenous equation, i.e A_{n+1}=8/9 A_{n}, then write a solution as:
    A{n}= A*(8/9)^n + B * (20/9)^n
    plug this solution to the equation to find B, and then plug n=0 A{0} to find A.
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