Question

an = 9 + (n−1)(2)

The rate of change of this linear function is the rate of change of this arithmetic sequence.

Answer 1

The rate of change of a linear function is equal to the common difference of the arithmetic sequence.

In this case, the linear function is an = 9 + (n−1)(2). To find the rate of change, we can first simplify the equation:

an = 9 + 2n − 2

Next, we can rearrange the equation to isolate the term with n on one side:

an - 9 = 2n - 2

Now, we can combine like terms:

an - 2n = 9 - 2

Simplifying further:

-an = 7

Finally, we can divide both sides of the equation by -1 to solve for n:

n = -7

Therefore, the rate of change of this linear function is -7, which means that the common difference of the arithmetic sequence is -7.