Un=100(Un-1) + 20(Un-2) ?!
I have tried to start solving and I get
U(x) (1-100x-20x^2) -100 -20x = 0
but after that it looks impossible to get something of the form 1/ (1-ax) ...
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A method to solve such equations is described in this Wikipedia article. Look for the paragraph that starts with "Consider, for example, a recurrence relation of the form ."
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