Answer:
[tex]a_{n}[/tex] = [tex]\frac{1}{4}[/tex][tex]a_{n-1}[/tex]
Step-by-step explanation:
The recursive rule allows us to find the term in a sequence from the previous term by multiplying it by the common ratio.
The common ratio r for the geometric sequence is
r = [tex]\frac{\frac{1}{2} }{2}[/tex] = [tex]\frac{1}{4}[/tex]
Thus the recursive rule is
[tex]a_{n}[/tex] = [tex]\frac{1}{4}[/tex][tex]a_{n-1}[/tex] with a₁ = 2
