Final answer:
The explicit rule for the given geometric sequence is an = 9 × (2/3)^(n-1), where an is the nth term, 9 is the first term, and 2/3 is the common ratio.
Step-by-step explanation:
The explicit rule for a geometric sequence can be found by identifying the common ratio between consecutive terms. In this case, since the sequence is 9, 6, 4, ..., we can start by dividing the second term by the first term (6/9 = 2/3) and the third term by the second term (4/6 = 2/3), confirming that the common ratio is 2/3. Therefore, the explicit rule for an nth term, an, of this geometric sequence with the initial term a being 9 (a1 = 9) and common ratio r being 2/3 is given by an = 9 × (2/3)n-1.