Question

Lesson 4.03

Answer 1

Using a geometric sequence, it is found that:

a) The explicit formula is: $a_n = 250000(2.1)^{n-1}$.

b) The value of her collection 9 years after she started tracking is of $94,557,148.

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.

Item a:

Three years ago, her collection was worth $250,000, hence the first term is $a_1 = 250000$.

In two years, the collection was valued at $1,102,500, hence the common ratio is:

$q^2 = \frac{1,102,500}{250,000}$

$q^2 = 4.41$

$q = \sqrt{4.41} = 2.1$.

Hence, the explicit formula is:

$a_n = 250000(2.1)^{n-1}$

Item b:

$a_9 = 250000(2.1)^{9-1} = 94557148$

The value of her collection 9 years after she started tracking is of $94,557,148.

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