Final answer:
The recursive rule for this geometric sequence is a_n = a_(n-1) * r, where a_n represents the nth term, a_(n-1) represents the previous term, and r represents the common ratio. In this case, the common ratio is 3.
Step-by-step explanation:
The recursive rule for this geometric sequence is:
an = an-1 * r
where an represents the n-th term in the sequence, an-1 represents the previous term in the sequence, and r represents the common ratio between consecutive terms.
In this case, the common ratio (r) can be calculated by dividing any term by its preceding term. For example, 21 ÷ 7 = 3, 63 ÷ 21 = 3, and 189 ÷ 63 = 3. Therefore, the common ratio is 3.
Using the recursive rule, we can express the sequence as
an = an-1 * 3