Consider the following difference equation and initial condition(s). In each case, verify that the expression given for an (i) is a solution of the equation (ii) satisfies the initial condition(s).
(a) an = 2(1/3)n satisfies 3an = an-1, a0 = 2.
(b) an = 2n - n 2 satisfies an+1 - 3an + 2an-1 = 2n - 3, a0 = 1, a1 = 1.