$(15$ pts$)($Recurrence$)$ Find closed form formulae for $T_n.$

$($a$)(5$ pts$)T_0=1,T_1=0,T_n=5T_{n-1}-6T_{n-2}$ for $n2.$

$($b$)(5$ pts$)T_0=1,T_1=2,T_n=-6T_{n-1}-9T_{n-2}$ for $n2.$

$($c$)$ pts$)T_0=T_1=0,$

$T_n=\frac{1}{2}(T_{n-1}+T_{n-2})+1$

for $n2.($Hint: Let $S_n=T_n+an$ and choose a such that $S_n$ satisfies a linear homogeneous

recurrence.$)$