Consider the sequence $7,11,15,19,23,$dots with $a_1=7.$

a$.$ Which of the following is a recursive definition for the sequence. Select all that apply.

A$.a_n=4*a_{n-1}$;$a_1=7$

B$.a_n=a_{n-1}+a_{n-2}$;$a_1=7$

C$.a_n=7*4^n$

D$.a_n=a_{n-1}+4$;$a_1=7$

b$.$ Give a closed formula for the $n$th term of the sequence.

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c$.$ Is $2051$ a term in the sequence?

A$.$ No$,$ it is between $2049$ and $2053$

B$.$ Yes, it is $a_{2051}$

C$.$ Yes, it is $a_{511}$

D$.$ Yes, it is $a_{512}$

E$.$ No$,$ it is larger than $587$