a_{n} = - 4 + 6(n - 1)
A. rate of change (common difference) of -4
B. initial value of 6
C. rate of change (common difference) of 6
C. rate of change (common difference) of 6
f(x) = - 4x + 2
A. rate of change (common difference) of -4
B. initial value of 6
A. rate of change (common difference) of -4
a_{n} = 6 + 7(n - 1)
A. rate of change (common difference) of -4
B. initial value of 6
C. rate of change (common difference) of 6
C. rate of change (common difference) of 6
To find the rate of change (common difference) of a sequence, you need to compare the values of consecutive terms and see how much they differ by. In this case, we have the sequence given by the formula a_n = -4 + 6(n - 1).
To find the rate of change (common difference), we need to look at the difference between consecutive terms. Let's calculate the values of the sequence for two consecutive values of n:
When n = 1:
a₁ = -4 + 6(1 - 1) = -4 + 6(0) = -4 + 0 = -4
When n = 2:
a₂ = -4 + 6(2 - 1) = -4 + 6(1) = -4 + 6 = 2
The sequence values for n = 1 and n = 2 are -4 and 2, respectively. The difference between these two terms is 2 - (-4) = 6.
Therefore, the common difference (rate of change) of the sequence is 6, which means option C is the correct answer.