Question

Calculate the average rate of change for the graphed sequence from n = 2 to n = 4.

graphed sequence showing (1, -3), (2, -3.5), (3, -6.75), (4, -10.125), (5, -15.1875), (6, -22.78125) A. -6.625

B. -03.3125

C. -3.0

D. -2.0

Answer 1

option: B is correct.

Explanation:

we are given the coordinates (x,y) as:

(1,-3),(2,-3.5),(3,-6.75),(4,-10.125),(5,-15.1875),(6,-22.78125).

The average rate of change from
`(x_(1),y_(1))` to
`(x_(2),y_(2))` is defined as:

`(y_(2)- y_(1) )/(x_(2)-x_(1))`

here we are asked to find the average rate of change for the graphed sequence from n=2 to n=4.

i.e. we need to find average rate of change from (2,-3.5) to (4,-10.125) is given by:

`(-10.125-(-3.5))/(4-2)\\ \\=(-6.625)/(2)\\ \\=-3.3125`.

Hence the average rate of change from n=2 to n=4 is: -3.3125.

Hence, option B is correct.

Answer 2

Average rate of chage = [change of y] / [change of x] = [- 10.125 - (-.35)] /[4 - 2] =

= -3.3125

Answer: option B.