Respuesta :
The given sequence is a geometric sequence and the next three terms are
-4, 2, -1
i.e 32, -16, 8, -4, 2, -1.
So option d is our correct answer.
The given sequence is 32, -16, 8, ...
We need to find what type of sequence is 32, -16, 8,... and calculate the next three terms that satisfy the given sequence.
i.e we need to find the [tex]4^{th},5^{th}~and~6^{th}~ term~of~the~sequence.[/tex]
What is a geometric sequence?
It is a sequence in which each term is found by multiplying the preceding term by a constant value 'r' called the common ratio.
Example: 4,8,16,32 where r = 2.
The formula used to find the nth term in a geometric sequence is:
[tex]a_n = a_1 ~r^{n-1}[/tex] Where a_1 is the first term of the sequence.
We have the given sequence as 32, -16, 8,......
Find the common ratio.
r = -16 / 32 = -1 / 2r = 8 /-16 = -1 / 2
Here we see that each term is found by multiplying the previous term with a common ratio r = -1/2.
So the given sequence is a geometric sequence.
Here a_1 = 32.
Applying the nth term geometric sequence to find the [tex]4^{th},5^{th}~and~6^{th}~ term~of~the~sequence.[/tex]
We get,
[tex]a_4=a_1(\frac{-1}{2})^{4-1}\\\\a_4=32(\frac{-1}{2})^3\\\\a_4 = \frac{-32}{8}\\\\a_4=-4\\\\a_5=a_1(\frac{-1}{2})^{5-1}\\\\a_5=32(\frac{-1}{2})^4\\\\a_5 = \frac{32}{16}\\\\a_5=2\\\\a_6=a_1(\frac{-1}{2})^{6-1}\\\\a_6=32(\frac{-1}{2})^5\\\\a_6 = \frac{-32}{32}\\\\a_6=-1\\[/tex]
We see that the sequence is 32, -16, 8, -4, 2, -1.
The given sequence is a geometric sequence and the next three terms are -4, 2 and -1
i.e 32, -16, 8, -4, 2, -1
Learn more about geometric sequences here:https://brainly.com/question/11266123
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