Asequence is defined by the recursive formula f(n + 1) = 1.5f(n). which sequence could be generated using the formula?

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Asequence is defined by the recursive formula f(n + 1) = 1.5f(n). which sequence could be generated using the formula?

The way to think about this recursive definition is to see that f(n + 1) refers to "the next number in the sequence", which in this case is defined as 1.5 f(n), or simply put, it is 1.5 times larger than the previous number.

The easiest way to think of this is to simply take the current number and multiple it by 1.5 to get the next number in the sequence.

If you begin the sequence with the number 1, this could become:

1

1.5

2.25

3.375

5.0625

and so forth.

Hope this helps!

Good luck

The sequence -12 , -18 , -27 , is generated using the formula ⇒ 1st sequence

Step-by-step explanation:

The recursive formula of the sequence is f(n + 1) = 1.5 f(n)

That means there is a constant ratio 1.5 between each two consecutive terms

In sequence -12 , -18 , -27 ,

The first term is -12

The formula is f(n + 1) = 1.5 f(n)

Use the first term where n = 1 to find the 2nd term

∵ f(1) = -12

- Substitute n by 1 in the given formula

∵ f(1 + 1) = 1.5 f(1)

∴ f(2) = 1.5(-12)

∴ f(2) = -18

Use the second term where n = 2 to find the 3rd term

∵ f(2) = -18

- Substitute n by 2 in the given formula

∵ f(2 + 1) = 1.5 f(2)

∴ f(3) = 1.5(-18)

∴ f(3) = -27

∴ The sequence -12 , -18 , -27 , is generated using the formula

It is -16, 17.5, -19, ...

The way to think about this recursive definition is to see that f(n + 1) refers to "the next number in the sequence", which in this case is defined as 1.5 f(n), or simply put, it is 1.5 times larger than the previous number.

The easiest way to think of this is to simply take the current number and multiple it by 1.5 to get the next number in the sequence.

If you begin the sequence with the number 1, this could become:

1

1.5

2.25

3.375

5.0625

and so forth.

Hope this helps!

Good luck

a

Step-by-step explanation:

I think 12, -18, -27 I’m not sure

Formula f(n+1) = 1.5 f(n) => f(n+1) / f(n) = 1.5. That means, that you have to search for a sequence where the ratio of two consecutive terms is 1.5. The first sequence is the only one that meets that: - 18 / - 12 = 1.5 and - 27 / - 18 = 1.5. So, the answer is the first option: -12, -18, -27, ...

We're analyzing each case to determine the solution.

we know that the sequence's formula is

[tex]f(n + 1) = 1.5f(n)[/tex]

case a)

we have the sequence

[tex]-12,-18,-27,...[/tex]

Let

[tex]f(1)=-12[/tex]

with the formula find the value of [tex]f(2)[/tex] and [tex]f(3)[/tex] and compare

Find the value of [tex]f(2)[/tex]

[tex]n=1[/tex]

[tex]f(1 + 1) = 1.5f(1)[/tex]

[tex]f(2) = 1.5*(-12)=-18[/tex]

Find the value of [tex]f(3)[/tex]

[tex]n=2[/tex]

[tex]f(2 + 1) = 1.5f(2)[/tex]

[tex]f(3) = 1.5*(-18)=-27[/tex]

therefore

The sequence case a) could be generated using the formula

case b)

we have the sequence

[tex]-20,30,-45,...[/tex]

Let

[tex]f(1)=-20[/tex]

with the formula find the value of [tex]f(2)[/tex] and [tex]f(3)[/tex] and compare

Find the value of [tex]f(2)[/tex]

[tex]n=1[/tex]

[tex]f(1 + 1) = 1.5f(1)[/tex]

[tex]f(2) = 1.5*(-20)=-30[/tex]

Find the value of [tex]f(3)[/tex]

[tex]n=2[/tex]

[tex]f(2 + 1) = 1.5f(2)[/tex]

[tex]f(3) = 1.5*(-30)=-45[/tex]

therefore

The sequence case b) could not be generated using the formula

case c)

we have the sequence

[tex]-18,-16.5,-15,...[/tex]

Let

[tex]f(1)=-18[/tex]

with the formula find the value of [tex]f(2)[/tex] and [tex]f(3)[/tex] and compare

Find the value of [tex]f(2)[/tex]

[tex]n=1[/tex]

[tex]f(1 + 1) = 1.5f(1)[/tex]

[tex]f(2) = 1.5*(-18)=-27[/tex]

Find the value of [tex]f(3)[/tex]

[tex]n=2[/tex]

[tex]f(2 + 1) = 1.5f(2)[/tex]

[tex]f(3) = 1.5*(-27)=-40.5[/tex]

therefore

The sequence case c) could not be generated using the formula

case d)

we have the sequence

[tex]-16,-17.5,-19,...[/tex]

Let

[tex]f(1)=-16[/tex]

with the formula find the value of [tex]f(2)[/tex] and [tex]f(3)[/tex] and compare

Find the value of [tex]f(2)[/tex]

[tex]n=1[/tex]

[tex]f(1 + 1) = 1.5f(1)[/tex]

[tex]f(2) = 1.5*(-16)=-24[/tex]

Find the value of [tex]f(3)[/tex]

[tex]n=2[/tex]

[tex]f(2 + 1) = 1.5f(2)[/tex]

[tex]f(3) = 1.5*(-24)=-36[/tex]

therefore

The sequence case d) could not be generated using the formula

therefore

the answer is

The sequence case a) could be generated using the formula

[tex]-12,-18,-27,...[/tex]

Answer is A. –12, –18, –27, ...

Step-by-step explanation:

the first one

I mean -12,-18,-28

because it fits the equation