B
The n th term ( explicit formula) for a geometric sequence is
[tex]a_{n}[/tex] = [tex]a_{1}[/tex][tex](r)^{n-1}[/tex]
where [tex]a_{1}[/tex] is the first term and r the common ratio, hence
[tex]a_{1}[/tex] = 6 and r = - [tex]\frac{1}{4}[/tex]
The recursive formula lets us find the next term in the sequence from the previous term by multiplying the previous term by r, hence
[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex]( - [tex]\frac{1}{4}[/tex] )with [tex]a_{1}[/tex] = 6
