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Scarlett bought an ant farm with 80 ants. From the following week forward, the ant population tripled every week. Let g(n) be the number of ants in Scarlett's farm in the nth week since she got it. What kind of sequence is it?

1) Arithmetic sequence
2) Geometric sequence
3) Fibonacci sequence
4) Exponential sequence

User Stk
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1 Answer

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Final answer:

The ant population in Scarlett's farm, which triples every week, is an example of a geometric sequence.

Step-by-step explanation:

Scarlett's ant population, which starts with 80 ants and triples every week, represents a geometric sequence. This is because in a geometric sequence, each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

In Scarlett's case, the common ratio is 3, since the population triples each week. Specifically, g(n) = 80 × 3^{(n-1)}, where g(n) is the number of ants in the nth week, and the sequence starts with the first week as n = 1.

An arithmetic sequence, by contrast, consists of a series where each term is derived by adding a constant value, known as the common difference, to the previous term, which does not fit the pattern described.

A Fibonacci sequence is a specific type of sequence where each term is the sum of the two preceding terms, which again does not match Scarlett's situation.

Exponential sequences generally refer to sequences that can be described by an exponential function, but in the case of sequences that deal specifically with the multiplication of terms by a constant ratio, 'geometric sequence' is the more precise term.

User Sergey Sob
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