Answer:
The given geometric sequence is: 3, 3/2, 3/4, 3/8, ...
The recursive rule for a geometric sequence is given by \(a_n = r \cdot a_{n-1}\), where \(a_n\) is the nth term, \(r\) is the common ratio, and \(a_{n-1}\) is the previous term.
In this case, the common ratio \(r\) is \( \frac{1}{2} \) because each term is obtained by multiplying the previous term by \( \frac{1}{2} \).
So, the correct option is:
b. \(a_1 = \frac{3}{2}\); \(a_n = \frac{1}{2} \cdot a_{n-1}\)