contestada

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 :

Given:

The geometric sequence is:

[tex]n[/tex]              [tex]a_n[/tex]

1                        -4

2                      20

3                     -100

To find:

The explicit formula and list any restrictions to the domain.

Solution:

The explicit formula of a geometric sequence is:

[tex]a_n=ar^{n-1}[/tex]            ...(i)

Where, a is the first term, r is the common ratio and [tex]n\geq 1[/tex].

In the given sequence the first term is -4 and the second term is 20, so the common ratio is:

[tex]r=\dfrac{a_2}{a_1}[/tex]

[tex]r=\dfrac{20}{-4}[/tex]

[tex]r=-5[/tex]

Putting [tex]a=-4,r=-5[/tex] in (i), we get

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

Therefore, the correct option is B.

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