Question

The table below shows the value of Henry's car at the end for each of the first 3 years after it is purchased. The values form a geometric
sequence.
Year
Value
dollars)
18000
116200
14580
(in
What will be the approximate value of the car at the end of the 10th year?
O
A. $6,974
B. $8,610
C. $11,810
D. $7,748

Answer 1

Using a geometric sequence, it is found that the approximate value of the car at the end of the 10th year will be given by:

A. $6,974.

What is a geometric sequence?

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

$a_n = a_1q^{n-1}$

In which $a_1$ is the first term.

In this problem, the first term and the common ratio are given, respectively, by:

$a_1 = 18000, q = \frac{16200}{18000} = 0.9$

Hence the equation is:

$a_n = 18000(0.9)^{n-1}$

At the end of the 10th year, the value will be of:

$a_{10} = 18000(0.9)^{10-1} = 6974$

Hence option A is correct.

More can be learned about geometric sequences at brainly.com/question/11847927

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