Recurrence Relation for Alpha beta filter

[SpartanG345]

The alpha beta filter equation is given by this

Xni = AXn + BXn-1

Xn-1 is subscript

i want to figure the solution to this recurrence relation, but is it a recurrence relation?

i am wondering weather alpha beta filters grow faster than exponential smoothing filters.- i said it is a 1st order equation

where Xn = C1 (B/1-A)^n so alpha beta filtering grow polynomial
But i am not quite sure to find the grow rate of the exponential filtering equation

 

[SpartanG345]

sorry this is wrong, the alpha beta filter equation is not a recurrence relation..