Question

Which of the following is UNLIKE the others with respect to the rate of change (common difference)?
A. 2, 8, 12, 20, 26
B. f (x) = 6x + 1
C. an = -5 + 6 (n - 1)
D. f (x) = 6x - 2

Answer 1

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).