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For the following geometric sequence find the recursive 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 :

apologiabiology
first term (a1) is -1

recursive formula goes like this

[tex]a_n[/tex] is the nth term
[tex]a_{n-1}[/tex] is the term before that

we normally have [tex]a_n=f(a_{n-1})[/tex]

we see each term is multipying by -3 to get next one


so that would be
[tex]a_n=-3*a_{n-1}[/tex] where a1=-1


the 3rd option is correct except that it is the explicit formula

so answer is 2nd one

The recursive formula: {-1, 3, -9, ...} is an = -3 · an - 1 where a1 = -1

What is Geometric Progression?

A geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio, r.

Given sequence : {-1,3,-9,......}

As, a1 = (-1)

The recursive formula will be

[tex]a_n[/tex] is the nth term and [tex]a_(n-1)[/tex] is the term before that

Now, we know that

  [tex]a_n = f(a_(n-1)[/tex]

By observing the series we can see that the next number in the series can be obtained by multiplying the series with -3.

So, [tex]a_n = 3 * a_(n-_1)[/tex]

also, here a1 = -1

Hence, an = -3 · an - 1 where a1 = -1

Learn more about Geometric Progression here:

https://brainly.com/question/4853032

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