Given the recurrence an−4an−1+4an−2=0a_n - 4a_{n-1} + 4a_{n-2} = 0an−4an−1+4an−2=0, what is the general solution for the sequence?
an=c12n+c24na_n = c_1 2^n + c_2 4^nan=c12n+c24n
an=c12n+c2n2na_n = c_1 2^n + c_2 n 2^nan=c12n+c2n2n
an=c14n+c2n4na_n = c_1 4^n + c_2 n 4^nan=c14n+c2n4n
an=(c1+c2n)4na_n = (c_1 + c_2 n) 4^nan=(c1+c2n)4n