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].
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].
