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krek1111 [17]
2 years ago
15

WILL GIVE BRAINLIEST

Mathematics
1 answer:
Llana [10]2 years ago
3 0
ANSWER IS Z
........
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Which sequence is modeled by the graph below?
mariarad [96]

Answer:

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

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.

<u>General form</u> of a geometric sequence:

 a_n=ar^{n-1}

where:

  • a is the first term
  • r is the common ratio
  • a_n 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:

\implies r=\dfrac{a_3}{a_2}=\dfrac{3}{9}=\dfrac{1}{3}

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

\implies a_2=9

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

\implies \dfrac{1}{3}a=9

\implies a=27

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

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

Learn more about geometric sequences here:

brainly.com/question/25398220

brainly.com/question/27783194

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The wheel was first documented as being used in Mesopotamia
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5,172 years

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