Question

The value of a motorcycle each year follows the sequence $12,000 $9,600, $7,680, $6,144

Which formula represents the recursive definition of the sequence where n represents the number of years?

Answer 1

The recursive definition of the geometric sequence is given by:

A. $a_n = (0.8)a_{n-1}$

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 basic recursive relation is given as follows:

$a_n = qa_{n-1}$

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, considering the given sequence, the common ratio is given by:

$q = \frac{6144}{7680} = \frac{7680}{9600} = \frac{9600}{12000} = 0.8$

Hence option A is correct.

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

Answer 2

The values of the motorcycle follows a geometric sequence

The recursive definition of the sequence is (a) $a_{n} = 0.8a_{n-1$

How to determine the recursive definition?

The values are given as:

$12,000 $9,600, $7,680, $6,144

Calculate the common ratio using:

r = a2/a1

So, we have:

r = 9600/12000

Divide

r = 0.8

Recall that:

r = a2/a1

So, we have:

a2/a1 = 0.8

Multiply both sides by a1

a2 = 0.8a1

Rewrite as:

$a_{2} = 0.8a_{2-1$

Substitute n for 2

$a_{n} = 0.8a_{n-1$

Hence, the recursive definition of the sequence is (a) $a_{n} = 0.8a_{n-1$

Read more about sequence at:

https://brainly.com/question/7882626