Question

What is the average rate of change for the sequence shown below? (I added a picture)

The answer choices are:
A. −2
B. 2
C. −one half
D. one half

Answer 1

The average rate of change for the problem would be -1/2

Answer 2

Option C is correct

`-(1)/(2)`

Explanation:

Formula for slope is given by:

`\text{Slope} = (y_2-y_1)/(x_2-x_1)`

As per the statement:

Given the sequence as shown

(5, 1), (3, 2), (3, 1), (-1, 4) ,....

We have to find average rate of change or slope for the sequence.

Consider any two points from the sequence,

(5, 1), (3, 2)

here,
`x_1 = 5`,
`y_1 = 1`,
`x_2 = 3` and
`y_2= 2`

Apply the formula for slope we have;

`\text{Slope} = (2-1)/(3-5) = -(1)/(2)`

Therefore, the average rate of change for the sequence is,
`-(1)/(2)`