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The first four terms of a sequence are shown below: 9, 5, 1, â’3 Which of the following functions best defines this sequence? f(1) = 9, f(n 1) = f(n) â’ 4; for n ≥ 1 f(1) = 9, f(n 1) = f(n) 4; for n ≥ 1 f(1) = 9, f(n 1) = f(n) â’ 5; for n ≥ 1 f(1) = 9, f(n 1) = f(n) 5; for n ≥ 1.

Respuesta :

The function that best defines this arithmetic sequence is:

  • [tex]f(n) = f(n - 1) - 4, f(1) = 9[/tex]

What is an arithmetic sequence?

  • In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.

The recursive function that defines the sequence is:

[tex]f(n) = f(n - 1) + d[/tex]

[tex]f(1) = f_0[/tex]

  • In which [tex]f_0[/tex] is the first term.

In this problem, the sequence is: {9, 5, 1, -3}

  • Each term is the previous term subtracted by 4, hence [tex]d = -4[/tex].
  • The first term is 9, hence [tex]f_0 = 9[/tex].

Hence, the function is:

  • [tex]f(n) = f(n - 1) - 4, f(1) = 9[/tex]

You can learn more about arithmetic sequences at https://brainly.com/question/6561461

dwivedisiddhant03

To identify the functions which best define the given sequence, we have to identify the number pattern.

The correct option is (a).

Given:

The given sequence is as follows,

[tex]9,5,1,-3[/tex]

What is an arithmetic sequence?

The arithmetic sequence define as the difference between two consecutive number would be same.

If we subtract 4 form each digit we will get next digit.

[tex]9-4=5\\5-4=1\\1-4=-3[/tex]

So the function would be,

[tex]f(1) = 9, f(n + 1) = f(n) -4; \rm for \:n\geq 1[/tex]

The option (b) and (d) show the increasing function whereas we have decreasing sequence.

Thus, the correct option is (a).

Learn more about arithmetic sequence here

:https://brainly.com/question/12637273

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