Is there an effective way of finding a particular $x_n$, say $x_5$, of a system of difference equations $x_{n}=ax_{n+1}+bx_{n-1}$ where $a, b$ are constants and the $n$'s say are $\leq k$ (apart from actually substituting each equation into the next)? Thanks.
System of difference equations
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linear-algebra
recurrence-relations
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2You could solve the constant-coefficient linear difference equation explicitly. This is second-order, so your characteristic polynomial is quadratic... – 2011-10-13
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0@J.M.: Thanks. I am being silly. – 2011-10-13
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0See [this answer](http://math.stackexchange.com/questions/67386/linear-homogeneous-difference-equation-with-constant-coefficients/67418#67418) for a closed formula to solve such equations. – 2011-10-13
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0@Guesswhoitis. Please consider converting your comment into an answer, so that this question gets removed from the [unanswered tab](http://meta.math.stackexchange.com/q/3138). If you do so, it is helpful to post it to [this chat room](http://chat.stackexchange.com/rooms/9141) to make people aware of it (and attract some upvotes). For further reading upon the issue of too many unanswered questions, see [here](http://meta.stackexchange.com/q/143113), [here](http://meta.math.stackexchange.com/q/1148) or [here](http://meta.math.stackexchange.com/a/9868). – 2015-05-06