Final answer:
The correct explicit rule for the given geometric sequence is an = 9 × (2/3)^(n-1), matching option b from the provided choices.
Step-by-step explanation:
The question asks for the explicit rule of a geometric sequence where the first term, a1, is 2/3 and each term an is found by multiplying the previous term by 9. To find the explicit rule, we use the formula for a geometric sequence which is an = a1 × r^(n - 1), where a1 is the first term, r is the common ratio, and n is the term number. In this case, the first term is 2/3 and the common ratio is 9.
An explicit formula that fits this geometric sequence is: an = (2/3) × 9^(n-1). Therefore, the correct explicit rule for the given geometric sequence is option (b), which is written as an = 9 × (2/3)^(n-1).