Question

Write an explicit rule for the nth term of the geometric sequence. NO LINKS!!!!
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Answer 1

`7 \\ 5 * {1.1}^(x - 1) \\8 \\ (1)/(9) = a * {( - 3)}^(8 - 1) \\ a = (1)/(9) * \frac{ - 1}{ {3}^(7) } = \frac{ - 1}{ {3}^(9) } \\ \\ \frac{ - 1}{ {3}^(9) } * {( - 3)}^(x - 1)`

Answer 2

see explanation

Explanation:

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

`a_(n)` = a₁
`(r)^(n-1)`

where a₁ is the first term and r the common ratio

(7)

`a_(n)` = 5
`(1.1)^(n-1)`

(8)

Given a₈ =
`(1)/(9)` , then

a₁
`(-3)^(7)` =
`(1)/(9)`

a₁ × - 2187 =
`(1)/(9)` ( divide both sides by - 2187 )

a₁ = -
`(1)/(19683)`

Then

`a_(n)` = -
`(1)/(19683)`
`(-3)^(n-1)`