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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 · an - 1 where a1 = -1 an = -1 · (-3)n - 1 an = (-3)n - 1

Respuesta :

texaschic101
{ 1,-3,9...}

an = a1 * r^(n-1)
a1 = first term = 1
r = common ratio = -3

so ur formula is : an = 1 * -3^(n-1)

Answer:

The correct option is 4.

Step-by-step explanation:

The given geometric sequence is

{1, -3, 9, ...}

Here the first term of the sequence is 1 and the common ratio is

[tex]r=\frac{a_2}{a_1}=\frac{-3}{1}=-3[/tex]

The explicit formula of a geometric sequence is

[tex]a_n=ar^{n-1}[/tex]

In the given geometric sequence a=1 and r=-3.

Substitute a=1 and r=-3 in the above formula.

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

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

The explicit formula of given geometric sequence is [tex]a_n=(-3)^{n-1}[/tex].

Therefore the correct option is 4.

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