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Madame Pickney has a rather extensive art collection and the overall value of her collection has been increasing each year. Three years ago, her collection was worth $500,000. Two years ago, the value of the collection was $550,000 and last year, the collection was valued at $605,000.

Assume that the rate at which Madame Pickney’s art collection’s value increase remains the same as it has been for the last three years. The value of the art collection can be represented by a geometric sequence. The value of the collection three years ago is considered the first term in the sequence.

What explicit rule can be used to determine the value of her art collection n years after that?

From the data provided, we know the sequence is {500,000; 550,000; 605,000; ... }. [tex]So, a_1 = 500,000\ and\ r = \dfrac{550,000}{500,000}=1.1[/tex]

The explicit rule for a geometric sequence is: [tex]a_n=a_1(r)^{n-1}[/tex]

So, the explicit rule for the sequence above is: [tex]a_n=500,000(1.1)^{n-1}[/tex]

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maheshpatelvVT maheshpatelvVT · Answer 2 · 2022-06-08T10:27:28+02:00

The explicit rule is, 500000(1.1)ⁿ⁻¹ and it can be used to determine the value of her art collection n years option (A) is correct.

What is a sequence?

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

From the problem, we have sequence:

500000, 550000, 605000.....

The above sequence represents the geometric sequence

First term of the geometric sequence a = 500000

Common ratio r = 550000/500000 = 1.1

The explicit rule for a geometric sequence is:

[tex]\rm a(n) = a(r)^{n-1}[/tex]

[tex]\rm a(n) = 500000(1.1)^{n-1}[/tex]

Thus, the explicit rule is, 500000(1.1)ⁿ⁻¹ and it can be used to determine the value of her art collection n years.

Learn more about the sequence here:

brainly.com/question/21961097

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