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The explicit formula for the sequence is f(n)=-10(3)ⁿ is it arithmetic or geometric.

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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.

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