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Consider the geometric sequence: 8, 4, 2, 1, \dots8,4,2,1,…8, comma, 4, comma, 2, comma, 1, comma, dots If nnn is an integer, which of these functions generate the sequence? Choose all answers that apply: Choose all answers that apply: (Choice A, Checked) A a(n)=8\left(\dfrac12\right)^na(n)=8( 2 1 ​ ) n a, left parenthesis, n, right parenthesis, equals, 8, left parenthesis, start fraction, 1, divided by, 2, end fraction, right parenthesis, start superscript, n, end superscript for n\geq1n≥1n, is greater than or equal to, 1 (Choice B) B b(n)=32\left(\dfrac12\right)^nb(n)=32( 2 1 ​ ) n b, left parenthesis, n, right parenthesis, equals, 32, left parenthesis, start fraction, 1, divided by, 2, end fraction, right parenthesis, start superscript, n, end superscript for n\geq2n≥2n, is greater than or equal to, 2 (Choice C) C c(n)=64\left(\dfrac12\right)^nc(n)=64( 2 1 ​ ) n c, left parenthesis, n, right parenthesis, equals, 64, left parenthesis, start fraction, 1, divided by, 2, end fraction, right parenthesis, start superscript, n, end superscript for n\geq3n≥3n, is greater than or equal to, 3 (Choice D, Checked) D d(n)=128\left(\dfrac12\right)^nd(n)=128( 2 1 ​ ) n d, left parenthesis, n, right parenthesis, equals, 128, left parenthesis, start fraction, 1, divided by, 2, end fraction, right parenthesis, start superscript, n, end superscript for n\geq4n≥4

Consider the geometric sequence 8 4 2 1 dots84218 comma 4 comma 2 comma 1 comma dots If nnn is an integer which of these functions generate the sequence Choose class=

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Answer:

C AND D

Step-by-step explanation:

KHAN ACADEMY.

C: c(n)= 64(1/2)^n for n greater than or equal to 3

D: d(n)= 128(1/2)^n for n greater than or equal to 4

The correct series is being generated by options B and D

What is geometric series?

A geometric series is a series for which the ratio of each two consecutive terms is a constant term called the common ratio.

How to find which of the given functions generate the given sequence?

  • We know that nth term of a Geometric series can be written as  [tex]ar^{n-1}[/tex] where a is the first term and r is the common ratio.

The given series is 8 , 4 , 2 , 1......

  • Here the first term is 8 and the common ratio is 1/2

Here, we should check the options one by one

  • The first option does not generate the series after putting values which are greater than or equal to 1

So, option A is wrong.

  • Now, if we put n = 2, 3 ... values in second function, we can see the series being generated.

So, option B is correct.

  • In option 3 if we put n = 3 then c(n) is coming as 8 but again on putting n = 4 , c(n) is coming 2.
  • So the series in not getting generated here.

Hence option C is wrong.

  • In option 4, we can see that the series is getting generated after putting the values n = 4,5.....

So, option D is correct.

Find more about "Geometric Series" here: https://brainly.com/question/24643676

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