Final answer:
The given sequence is an example of an exponential sequence, where each term is obtained by multiplying the previous term by a common ratio. The explicit and recursive forms of the sequence can be determined using formulas. The explicit form uses the position of the term and the common ratio, while the recursive form uses the previous term and the common ratio.
Step-by-step explanation:
The given sequence is an example of an exponential sequence, where each term is obtained by multiplying the previous term by a common ratio. In this case, the common ratio is 3, since each term is 3 times larger than the previous term.
The explicit form of the sequence can be found using the formula:
an = a1 * r(n-1)
where an is the n-th term, a1 is the first term, r is the common ratio, and n is the position of the term in the sequence.
For example, to find the explicit form of the 5th term:
a5 = 9 * 3(5-1) = 9 * 81 = 729
The recursive form of the sequence can be found using the formula:
an = an-1 * r
where an is the n-th term, an-1 is the previous term, and r is the common ratio.