Consider the recurrence an=2an−1−an−2a_n = 2a_{n-1} - a_{n-2}an=2an−1−an−2. What is the general solution?
an=c1+c2na_n = c_1 + c_2 nan=c1+c2n
an=c12n+c2a_n = c_1 2^n + c_2an=c12n+c2
an=c1n+c22na_n = c_1 n + c_2 2^nan=c1n+c22n
an=c1+c2n2a_n = c_1 + c_2 n^2an=c1+c2n2