ANSWER
The correct answer is B)
[tex]a_n=4( \frac{1}{3} )^{n-1}[/tex]
EXPLANATION
The recursive formula for the geometric sequence is
[tex]a_n= \frac{1}{3} a_{n-1}[/tex]
where,
[tex]a_1 = 4[/tex]
This implies that,
[tex]a_2= \frac{1}{3} a_{2-1}[/tex]
[tex]a_2= \frac{1}{3} a_{1}[/tex]
[tex]a_2= \frac{1}{3} \times 4 = \frac{4}{3} [/tex]
The explicit rule is of the form,
[tex]a_n=a_1r^{n-1}[/tex]
where
[tex]r = \frac{ a_{2}}{ a_{1}} [/tex]
[tex]r = \frac{ \frac{4}{3} }{ 4} [/tex]
[tex]r = \frac{4}{3} \times \frac{1}{4} = \frac{1}{3} [/tex]
The explicit rule is given by,
[tex]a_n=4( \frac{1}{3} )^{n-1}[/tex]
