Any one plz answer this (signal processing) question?

Q) Consider the first-order linear system defined by the difference equation y(n)=ay(n-1)=x(n),where the coefficient a is between zero and unity.The input x(n) is restricted to be a periodic sequence with period N;ie., ~x(n)=~x(n+kN) for any integer value

k.The lter output is assumed to have reached steady state .Determine,in terms of the

coefficient a,the unit-sample response for a nite impulse responselter which for this class

of inputs yields an output ~y(n) indistinguishable in steady state from the innite impulse

response filter defined by the above dieffrence equation.