Answer :
To determine which function produces the given sequence of numbers, let's identify the pattern in the sequence and use each provided function to see which one fits.
The sequence given is: 26, 35, 44, 53, 62.
1. Identify the pattern:
- The sequence is increasing.
- Calculate the differences between each consecutive pair:
- 35 - 26 = 9
- 44 - 35 = 9
- 53 - 44 = 9
- 62 - 53 = 9
- The differences between terms are consistent, each equal to 9, indicating a linear relationship.
2. Test each function:
A. [tex]\( f(n) = 26 - 9n \)[/tex]
- For [tex]\( n = 1 \)[/tex]: [tex]\( f(1) = 26 - 9 \times 1 = 17 \)[/tex] (Not matching 26)
B. [tex]\( f(n) = 9n + 17 \)[/tex]
- Calculate the first five terms:
- 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]
- All calculated terms match the given sequence.
C. [tex]\( f(n) = 17 - 9n \)[/tex]
- For [tex]\( n = 1 \)[/tex]: [tex]\( f(1) = 17 - 9 \times 1 = 8 \)[/tex] (Not matching 26)
D. [tex]\( f(n) = 9n + 26 \)[/tex]
- For [tex]\( n = 1 \)[/tex]: [tex]\( f(1) = 9 \times 1 + 26 = 35 \)[/tex] (Not matching 26)
3. Conclusion:
The function [tex]\( f(n) = 9n + 17 \)[/tex] correctly produces the sequence: 26, 35, 44, 53, 62. Therefore, the correct answer is B. [tex]\( f(n) = 9n + 17 \)[/tex].
The sequence given is: 26, 35, 44, 53, 62.
1. Identify the pattern:
- The sequence is increasing.
- Calculate the differences between each consecutive pair:
- 35 - 26 = 9
- 44 - 35 = 9
- 53 - 44 = 9
- 62 - 53 = 9
- The differences between terms are consistent, each equal to 9, indicating a linear relationship.
2. Test each function:
A. [tex]\( f(n) = 26 - 9n \)[/tex]
- For [tex]\( n = 1 \)[/tex]: [tex]\( f(1) = 26 - 9 \times 1 = 17 \)[/tex] (Not matching 26)
B. [tex]\( f(n) = 9n + 17 \)[/tex]
- Calculate the first five terms:
- 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]
- All calculated terms match the given sequence.
C. [tex]\( f(n) = 17 - 9n \)[/tex]
- For [tex]\( n = 1 \)[/tex]: [tex]\( f(1) = 17 - 9 \times 1 = 8 \)[/tex] (Not matching 26)
D. [tex]\( f(n) = 9n + 26 \)[/tex]
- For [tex]\( n = 1 \)[/tex]: [tex]\( f(1) = 9 \times 1 + 26 = 35 \)[/tex] (Not matching 26)
3. Conclusion:
The function [tex]\( f(n) = 9n + 17 \)[/tex] correctly produces the sequence: 26, 35, 44, 53, 62. Therefore, the correct answer is B. [tex]\( f(n) = 9n + 17 \)[/tex].
