Linear recurrence = closed form?

[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

 

[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.