For each sequence described below, circle the form of the closed formula and briefly explain.

Then write down the system of equations you would need to solve to find the constants $a,b,$

etc. $($You do not need to find the constants.$)$

$($a$)$ The sequence $(a_n{)}_{n}0$ with recursive definition $a_n=a_{n-1}+(n^2+3)$;$a_0=1.$

$($The sequence starts $1,5,12,24,45,$dots..$)$

A$.a{n}^2+bn+c$

B$.a{n}^3+b{n}^2+cn+d$

C$.a{3}^n+b(-1{)}^n$

D$.a{2}^n+b{3}^n$

Briefly explain:

$($b$)$ The sequence $(b_n{)}_{n}0$ with recursive definition $b_n=5b_{n-1}-6b_{n-2}$;$b_0=1,b_1=4.$

$($The sequence starts $1,4,14,46,146,$dots.$)$

A$.a{n}^2+bn+c$

B$.a{n}^3+b{n}^2+cn+d$

C$.a{3}^n+b(-1{)}^n$

D$.a{2}^n+b{3}^n$

Briefly explain: