To determine which of the options is unlike the others with respect to the rate of change (common difference), we need to analyze the nature of each option.
A. 2, 8, 12, 20, 26: This is a sequence. We calculate the differences between consecutive terms:
- 8 - 2 = 6
- 12 - 8 = 4
- 20 - 12 = 8
- 26 - 20 = 6
The differences are not constant, so this sequence does not have a common difference.
B. f(x) = 6x + 1: This is a linear function. The coefficient of x (6) is the rate of change, which is constant (6). This indicates a common difference of 6.
C. an = -5 + 6(n - 1): This expression defines a sequence. We can rewrite it as: \( an = 6n - 5 - 6 = 6n - 11 \) This is a linear function as well, indicating a common difference of 6.
D. f(x) = 6x - 2: This is another linear function. The rate of change (common difference) here is also 6.
Now, summarizing:
- A does not have a common difference, while B, C, and D have a constant rate of change of 6.
Therefore, the answer is: A. 2, 8, 12, 20, 26 is UNLIKE the others with respect to the rate of change (common difference).
3 answers