Question

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.

Answer 1

The function that best defines this arithmetic sequence is:

• $f(n) = f(n - 1) - 4, f(1) = 9$

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:

$f(n) = f(n - 1) + d$

$f(1) = f_0$

• In which $f_0$ is the first term.

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

• Each term is the previous term subtracted by 4, hence $d = -4$.

• The first term is 9, hence $f_0 = 9$.

Hence, the function is:

• $f(n) = f(n - 1) - 4, f(1) = 9$

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

Answer 2

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,

$9,5,1,-3$

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.

$9-4=5\\5-4=1\\1-4=-3$

So the function would be,

$f(1) = 9, f(n + 1) = f(n) -4; \rm for \:n\geq 1$

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

:brainly.com/question/12637273