6a1:

(a) $b_n-3b_{n-1}=n3^n-3(n-1)3^{n-1}=3^n(n-n+1)=3^n$

(b) $b_n-6b_{n-1}+9b_{n-2}=3^n(n-2n+2+n-2)=0$

6a2:

$(\mathrm{iii})$$d_n=d_{n-1}+6d_{n-2}$

6a3:

$(\mathrm{ii}) \ a_n=4a_{n-1}-4a_{n-2}$

$(\mathrm{iv}) a_n=7a_{n-1}-16a_{n-2}+12a_{n-3}$