Question 116
a. Using the characteristic equation method or otherwise, find a formula in terms of $n$ for the sequence $a_0 = 1$, $a_1 = 4$ and $a_{n+2} = 5a_{n+1} - 6a_n$ for $n = 0, 1, 2, \dots$
b. Using the characteristic equation method or otherwise, find a formula in terms of $n$ for the sequence $b_0 = 3$, $b_1 = 7$ and $b_{n+2} = 4b_{n+1} - 4b_n$ for $n = 0, 1, 2, \dots$
b. Using the characteristic equation method or otherwise, find a formula in terms of $n$ for the sequence $b_0 = 3$, $b_1 = 7$ and $b_{n+2} = 4b_{n+1} - 4b_n$ for $n = 0, 1, 2, \dots$