College

Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ The first 5 numbers of a sequence are shown below. Which of the following functions produces the sequence for [tex]n: \{1, 2, \ldots, n\}[/tex]?

[tex]26, 35, 44, 53, 62, \ldots[/tex]

A. [tex]f(n) = 17 - 9n[/tex]

B. [tex]f(n) = 9n + 26[/tex]

C. [tex]f(n) = 9n + 17[/tex]

D. [tex]f(n) = 26 - 9n[/tex]

Answer :

To determine which function produces the given sequence [tex]\(26, 35, 44, 53, 62, \ldots\)[/tex], let's go through each function option provided:

The sequence provided is:

1. [tex]\( 26 \)[/tex]
2. [tex]\( 35 \)[/tex]
3. [tex]\( 44 \)[/tex]
4. [tex]\( 53 \)[/tex]
5. [tex]\( 62 \)[/tex]

Let's evaluate each function option:

- Option A: [tex]\( f(n) = 17 - 9n \)[/tex]
Substituting the values of [tex]\( n = 1, 2, 3, 4, 5 \)[/tex]:
- For [tex]\( n = 1 \)[/tex]: [tex]\( f(1) = 17 - 9 \times 1 = 8 \)[/tex]
- For [tex]\( n = 2 \)[/tex]: [tex]\( f(2) = 17 - 9 \times 2 = -1 \)[/tex]
- For [tex]\( n = 3 \)[/tex]: [tex]\( f(3) = 17 - 9 \times 3 = -10 \)[/tex]
- For [tex]\( n = 4 \)[/tex]: [tex]\( f(4) = 17 - 9 \times 4 = -19 \)[/tex]
- For [tex]\( n = 5 \)[/tex]: [tex]\( f(5) = 17 - 9 \times 5 = -28 \)[/tex]

The results [tex]\(8, -1, -10, -19, -28\)[/tex] do not match the given sequence.

- Option B: [tex]\( f(n) = 9n + 26 \)[/tex]
Substituting the values of [tex]\( n = 1, 2, 3, 4, 5 \)[/tex]:
- For [tex]\( n = 1 \)[/tex]: [tex]\( f(1) = 9 \times 1 + 26 = 35 \)[/tex]
- For [tex]\( n = 2 \)[/tex]: [tex]\( f(2) = 9 \times 2 + 26 = 44 \)[/tex]
- For [tex]\( n = 3 \)[/tex]: [tex]\( f(3) = 9 \times 3 + 26 = 53 \)[/tex]
- For [tex]\( n = 4 \)[/tex]: [tex]\( f(4) = 9 \times 4 + 26 = 62 \)[/tex]
- For [tex]\( n = 5 \)[/tex]: [tex]\( f(5) = 9 \times 5 + 26 = 71 \)[/tex]

The sequence [tex]\(35, 44, 53, 62, 71\)[/tex] does not match the given sequence starting from the first term.

- Option C: [tex]\( f(n) = 9n + 17 \)[/tex]
Substituting the values of [tex]\( n = 1, 2, 3, 4, 5 \)[/tex]:
- For [tex]\( n = 1 \)[/tex]: [tex]\( f(1) = 9 \times 1 + 17 = 26 \)[/tex]
- For [tex]\( n = 2 \)[/tex]: [tex]\( f(2) = 9 \times 2 + 17 = 35 \)[/tex]
- For [tex]\( n = 3 \)[/tex]: [tex]\( f(3) = 9 \times 3 + 17 = 44 \)[/tex]
- For [tex]\( n = 4 \)[/tex]: [tex]\( f(4) = 9 \times 4 + 17 = 53 \)[/tex]
- For [tex]\( n = 5 \)[/tex]: [tex]\( f(5) = 9 \times 5 + 17 = 62 \)[/tex]

The results [tex]\(26, 35, 44, 53, 62\)[/tex] match the given sequence perfectly.

- Option D: [tex]\( f(n) = 26 - 9n \)[/tex]
Substituting the values of [tex]\( n = 1, 2, 3, 4, 5 \)[/tex]:
- For [tex]\( n = 1 \)[/tex]: [tex]\( f(1) = 26 - 9 \times 1 = 17 \)[/tex]
- For [tex]\( n = 2 \)[/tex]: [tex]\( f(2) = 26 - 9 \times 2 = 8 \)[/tex]
- For [tex]\( n = 3 \)[/tex]: [tex]\( f(3) = 26 - 9 \times 3 = -1 \)[/tex]
- For [tex]\( n = 4 \)[/tex]: [tex]\( f(4) = 26 - 9 \times 4 = -10 \)[/tex]
- For [tex]\( n = 5 \)[/tex]: [tex]\( f(5) = 26 - 9 \times 5 = -19 \)[/tex]

The results [tex]\(17, 8, -1, -10, -19\)[/tex] do not match the given sequence.

Therefore, the function that produces the sequence [tex]\(26, 35, 44, 53, 62, \ldots\)[/tex] is Option C: [tex]\( f(n) = 9n + 17 \)[/tex].