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Given a geometric sequence in the table below, create the explicit formula and list any restrictions to the domain.


n an
1 −4
2 20
3 −100

an = −5(−4)n − 1 where n ≥ 1
an = −4(−5)n − 1 where n ≥ 1
an = −4(5)n − 1 where n ≥ −4
an = 5(−4)n − 1 where n ≥ −4

Respuesta :

Answer:

B

Step-by-step explanation:

given the first 3 terms of the geometric sequence - 4, 20, - 100

with r = [tex]\frac{-100}{20}[/tex] = [tex]\frac{20}{-4}[/tex] = - 5

the n th term formula ( explicit formula ) is

[tex]a_{n}[/tex] = [tex]a_{1}[/tex] [tex]r^{n-1}[/tex]

here r = - 5 and [tex]a_{1}[/tex] = - 4, hence

[tex]a_{n}[/tex] = - 4 [tex](-5)^{n-1}[/tex] with n ≥ 1

This question is solved using geometric sequence concepts, and doing this, we get that the correct option is:

[tex]a_n = -4(-5)^{n-1}, n \geq 1[/tex], second option

Geometric sequence:

In a geometric sequence, the quotient between consecutive terms is the same, called common ration, and the general equation is given by:

[tex]a_n = a_1q^{n-1}, n \geq 1[/tex]

In which [tex]a_1[/tex] is the first term and q is the common ratio.

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n an

1 −4

2 20

3 −100

First term is -4, so [tex]a_1 = -4[/tex], then:

[tex]a_n = a_1q^{n-1}, n \geq 1[/tex]

[tex]a_n = -4q^{n-1}, n \geq 1[/tex]

The common ratio is:

[tex]q = \frac{-100}{20} = \frac{20}{-4} = -5[/tex]

Thus:

[tex]a_n = -4(-5)^{n-1}, n \geq 1[/tex] is the sequence.

A similar example is given at https://brainly.com/question/24078619

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