Respuesta :

Hamed313

Answer:

[tex]7 \\ 5 \times {1.1}^{x - 1} \\8 \\ \frac{1}{9} = a \times {( - 3)}^{8 - 1} \\ a = \frac{1}{9} \times \frac{ - 1}{ {3}^{7} } = \frac{ - 1}{ {3}^{9} } \\ \\ \frac{ - 1}{ {3}^{9} } \times {( - 3)}^{x - 1} [/tex]

Answer:

see explanation

Step-by-step explanation:

The nth term ( explicit rule ) of a geometric sequence is

[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]

where a₁ is the first term and r the common ratio

(7)

[tex]a_{n}[/tex] = 5 [tex](1.1)^{n-1}[/tex]

(8)

Given a₈ = [tex]\frac{1}{9}[/tex] , then

a₁ [tex](-3)^{7}[/tex] = [tex]\frac{1}{9}[/tex]

a₁ × - 2187 = [tex]\frac{1}{9}[/tex] ( divide both sides by - 2187 )

a₁ = - [tex]\frac{1}{19683}[/tex]

Then

[tex]a_{n}[/tex] = - [tex]\frac{1}{19683}[/tex] [tex](-3)^{n-1}[/tex]

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