What is the average rate of change for the sequence shown below?

Answer:
B
Step-by-step explanation:
The average rate of change can be found using formula
[tex]\dfrac{y_2-y_1}{x_2-x_1}.[/tex]
In your case,
[tex](x_1,y_1)=(4,-0.5),\\ \\(x_2,y_2)=(1,4).[/tex]
Hence,
[tex]\dfrac{-0.5-4}{4-1}=\dfrac{-4.5}{3}=-1.5=-1\dfrac{1}{2}.[/tex]
Answer: second option.
Step-by-step explanation:
The average rate of change is the slope, and this can be calculated with this formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Choose two points. Let's choose the points (1,4) and (3,1).
Now, substitute them into the formula [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]. Then you get:
[tex]m=\frac{1-4}{3-1}\\\\m=-\frac{3}{2}[/tex]
Rewrite this result as a mixed number. Therefore, the answer is:
[tex]m=-1\ \frac{1}{2}[/tex]
This matches with the second option.