Determine the Closed Form of a Recurrance Relation

Using this iteration method, I need to figure out the closed form for this reccurance relation:

T(n) = 2T(n - 10) + 3, for n > 11, T(n) = 5 for n <= 10


The answer is to be expressed exactly, using equality and not a bound or asymptomatic notation.

you can assume the following:

  • n = 10l +1 for some positive integer l
  • the expression does not need to be completely simplified, you can use either or both n and l in the solution
What i've gathered so far is the first 10 numbers in the sequence are 5, the next 10 numbers are equal to (2*previous number) + 3, so 13, and so on for every 10 terms. (correct?)

5 5 5 5 5 5 5 5 5 5 13 13 13 13 13 13 13 13 13 13 29 29 29 29 29 29 29 29 29 29 ...


Help in finding the closed form of this relation? preferably in terms of n , l and maybe both?

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