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 − 2
C. an = −5 + 6(n − 1)
f(x) = 6x +1
The rate of change for the arithmetic sequence A is +6 for each term. The rate of change for the linear function B is +6. The rate of change for the arithmetic sequence C is +6 for each term. However, the rate of change for the function f(x) is +6, which is unlike the others.
Therefore, the answer is $\boxed{\text{f(x) = 6x + 1}}$.
12 + 6 = 20 ?
Apologies for the mistake in my previous response. You are correct, the fourth term of the arithmetic sequence A should be 12 + 6 = 18, not 20.
In that case, the correct answer is A. 2, 8, 12, 20, 26. The rate of change (common difference) in this sequence is not constant, unlike the other options.
To find the answer, we need to determine the rate of change or the common difference for each given option.
A. 2, 8, 12, 20, 26:
To find the common difference for this sequence, we subtract each term from its preceding term: 8 - 2 = 6, 12 - 8 = 4, 20 - 12 = 8, 26 - 20 = 6. The common difference is not the same for all terms, so option A does not have a constant rate of change.
B. f(x) = 6x - 2:
This is an equation for a linear function. In the form y = mx + b, the slope (m) represents the rate of change. In this case, the slope is 6, meaning that for every increase of 1 in x, there is an increase of 6 in y. Since the slope is constant, the rate of change is the same for all values of x.
C. an = −5 + 6(n − 1):
This is an arithmetic sequence formula. The common difference is the coefficient of (n - 1), which is 6. Hence, the rate of change is constant.
D. f(x) = 6x +1:
Similar to option B, this is another equation for a linear function. The slope (rate of change) is 6 for every increase of 1 in x.
Based on the analysis above, option A is the only one that does not possess a constant rate of change (common difference).