Question

PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!

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 $600,000. Two years ago, the value of the collection was $690,000 and last year, the collection was valued at $793,500.

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?

Answer 1

Answer:an=600,000(1.15)^n−1

Explanation:

Answer 2

B. 600,000 (1.15)^{n-1}

Explanation:

The n-th term of a geometric sequence with initial value a and common ratio r can be determined by multiplying the first term of the sequence (i.e. initial value a) by r^{n-1}.

The first term (i.e. initial value a) is 600,000.

The common ratio r can be calculated by dividing any two consecutive terms in the sequence:

r = 690,000/600,000 = 1.15 or r = 793,500/690,000 = 1.15

Thus, we get the answer:

the explicit rule that can be used to determine the value of the art collection n years after that is 600,000 (1.15)^{n-1}