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For the following geometric sequence find the explicit formula: {-1, 3, -9, ...}. an = -3 · an - 1 where a1 = -1 an = (-3) n - 1 an = -3 · an - 1 where a1 = 1 an = -1 · (-3) n - 1

Respuesta :

Answer:

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

Step-by-step explanation:

The n th term ( explicit formula ) for a geometric sequence is

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

where a is the first term and r the common ratio

Here a = - 1 and r = - 9 ÷ 3 = 3 ÷ - 1 = - 3, thus

[tex]a_{n}[/tex] = - 1 [tex](-3)^{n-1}[/tex] with a₁ = - 1

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