Solve the following problem using Z-transform and check the answer using long division.
y(n) - 0.5y(n-1)+0.25y(n-2) = (1/3)ⁿ u(n)
Initial condition: y(-1) = 1, y(-2) = 0

a.) y(n) = (1/3)ⁿ + (1/3)(n-1)
b.) y(n) = (1/3)ⁿ - (1/3)(n-1)
c.) y(n) = (1/3)ⁿ + 2(1/3)(n-1)
d.) y(n) = (1/3)ⁿ - 2(1/3)(n-1)