Answered

Explore Westonci.ca, the leading Q&A site where experts provide accurate and helpful answers to all your questions. Connect with a community of experts ready to help you find accurate solutions to your questions quickly and efficiently. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

Which sequence is modeled by the graph below?

Which Sequence Is Modeled By The Graph Below class=

Sagot :

  • (2,9)
  • (3,3)
  • (4,1)

We can observe

  • 9/3=3
  • 3/3=1

Its a geometric progression having first term 9(3)=27 and common ratio as 1/3

So

The firmula is

  • a_n=27(1/3)^{n-1}

Option C

semsee45

Answer:

[tex]a_n=27\left(\dfrac{1}{3}\right)^{n-1}[/tex]

Step-by-step explanation:

From inspection of the graph, the given points are:

  • (2, 9)
  • (3, 3)
  • (4, 1)

If we draw a line through the given points, the line is a curve rather than a straight line. If the line was a straight line, the graph would be modeled as an arithmetic sequence. Therefore, as the line is a curve, the given points are modeling a geometric sequence.

General form of a geometric sequence:

 [tex]a_n=ar^{n-1}[/tex]

where:

  • a is the first term
  • r is the common ratio
  • [tex]a_n[/tex] is the nth term

Rewrite the given points as terms of the sequence:

  • (2, 9)  ⇒  a₂ = 9
  • (3, 3)  ⇒  a₃ = 3
  • (4, 1)  ⇒  a₄ = 1

To find the common ratio r, divide consecutive terms:

[tex]\implies r=\dfrac{a_3}{a_2}=\dfrac{3}{9}=\dfrac{1}{3}[/tex]

Calculate the first term (a) by substituting the found value of r and the given values of one of the terms into the formula:

[tex]\implies a_2=9[/tex]

[tex]\implies a\left(\dfrac{1}{3}\right)^{2-1}=9[/tex]

[tex]\implies \dfrac{1}{3}a=9[/tex]

[tex]\implies a=27[/tex]

Substitute the found values of r and a into the general formula to create the sequence modeled by the graph:

[tex]a_n=27\left(\dfrac{1}{3}\right)^{n-1}[/tex]

Learn more about geometric sequences here:

https://brainly.com/question/25398220

https://brainly.com/question/27783194

Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.