Question

HELP ME PLEASE

Identify the sequence graphed below and the average rate of change from n = 1 to n = 3.

an = 8(1/2)n − 1; average rate of change is −3
an = 10(1/2)n − 1; average rate of change is 3
an = 8(1/2)n − 1; average rate of change is 3
an = 10(1/2)n − 1; average rate of change is −3

Answer 1

The sequence is an = 8(1/2)^(n-1)

Average rate from n = 1 to n = 3 is -3

Its choice 1

Answer 2

Option A

Explanation:

To find nth term we use the given options.

`a_n= 8((1)/(2))^(n-1)`

Lets pick any point from the graph and plug it in the given option

LEts pick (1,8) and (2,4)

`a_n= 8((1)/(2))^(n-1)`, n=1, an=8

`8= 8((1)/(2))^(1-1)`

`8= 8((1)/(2))^(0)`

8=8 True

LEts check with (2,4), n=2 and an=4

`4= 8((1)/(2))^(2-1)`

4=4 True

Average rate of change from n=1 to n=3=
`(a_3-a_1)/(3-1) =(2-8)/(2) =-3`

Average rate of change from n=1 to n=3 is -3