The first 5 numbers of a sequence are shown below. Which of the following functions produces the sequence with [tex]$n:\{1,2, \ldots, n\}$[/tex]?

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

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

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

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

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

Sure, let's analyze the given sequence and determine which function fits it step by step.

The sequence provided is: [tex]$26, 35, 44, 53, 62, \ldots$[/tex]

We need to find which function from the given options produces this sequence for [tex]$n = \{1, 2, \ldots, n\}$[/tex].

Let's evaluate each option:

### Option A: [tex]$ f(n) = 17 - 9n $[/tex]

1. For [tex]$ n = 1 $[/tex]:
[tex]\[
f(1) = 17 - 9 \cdot 1 = 17 - 9 = 8
\][/tex]
This does not match 26. So, Option A is not correct.

### Option B: [tex]$ F(n) = 9n + 17 $[/tex]

1. For [tex]$ n = 1 $[/tex]:
[tex]\[
F(1) = 9 \cdot 1 + 17 = 9 + 17 = 26
\][/tex]
Matched!
2. For [tex]$ n = 2 $[/tex]:
[tex]\[
F(2) = 9 \cdot 2 + 17 = 18 + 17 = 35
\][/tex]
Matched!
3. For [tex]$ n = 3 $[/tex]:
[tex]\[
F(3) = 9 \cdot 3 + 17 = 27 + 17 = 44
\][/tex]
Matched!
4. For [tex]$ n = 4 $[/tex]:
[tex]\[
F(4) = 9 \cdot 4 + 17 = 36 + 17 = 53
\][/tex]
Matched!
5. For [tex]$ n = 5 $[/tex]:
[tex]\[
F(5) = 9 \cdot 5 + 17 = 45 + 17 = 62
\][/tex]
Matched!

All values match the given sequence. So, Option B is correct.

### Option C: [tex]$ f(n) = 9n + 26 $[/tex]

1. For [tex]$ n = 1 $[/tex]:
[tex]\[
f(1) = 9 \cdot 1 + 26 = 9 + 26 = 35
\][/tex]
This does not match 26. So, Option C is not correct.

### Option D: [tex]$ f(n) = 26 - 9n $[/tex]

1. For [tex]$ n = 1 $[/tex]:
[tex]\[
f(1) = 26 - 9 \cdot 1 = 26 - 9 = 17
\][/tex]
This does not match 26. So, Option D is not correct.

Therefore, the function that produces the given sequence is:

Option B: [tex]$ F(n) = 9n + 17 $[/tex]