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:
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:
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, ...
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