Final answer:
The sequence given by f(n) = -10(3)^n is geometric because each term is produced by multiplying the previous term by the common ratio of 3.
Step-by-step explanation:
The explicit formula for the sequence given is f(n) = -10(3)n. To determine whether the sequence is arithmetic or geometric, we must consider the nature of the sequence. An arithmetic sequence has a common difference between terms, whereas a geometric sequence has a common ratio.
In this formula, each term is generated by multiplying the previous term by 3, which is the common ratio here. The -10 in the formula is the initial term, and it does not affect the sequence type. Hence, since the terms of the sequence increase by a constant multiple rather than a constant addition, the sequence described by the formula f(n) = -10(3)n is geometric.