# Linear recurrence = closed form?

1. Apr 5, 2013

### mikeph

Hi

I've got a recurrence relation: x_n = a*x_(n-1) + b;

I think I'm going mad trying to figure out a closed form, eg. x(n) = ? the nth iteration

Is there a trick or something I'm missing?

Thanks

2. Apr 5, 2013

### jbunniii

Try writing out what you get for $x_1$, $x_2$, $x_3$ and see what the pattern is. Then take an educated guess and try to prove it by induction.

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