Question

The sequence an=1/2(2)^(n-1) is graphed below:

(2,1) (3,2) (4,4) (5,8)
Find the average rate of change between n=2 and n=4.
A 3/2
B 2/3
C 2
D 3

Answer 1

`(3)/(2)`.

Explanation:

Given :
`a_(n) = (1)/(2) * 2^(n-1)`

To find :Find the average rate of change between n=2 and n=4.

Solution : We have given that
`a_(n) = (1)/(2) * 2^(n-1)`.

The average rate of change of
`a_(n)` on interval [b,c] = that b =2 , c = 4 ,

Thus,
`(a_(b)-a_(c))/(b-c)` =
`((1)/(2)*(2)^(4-1) -(1)/(2)*(2)^(2-1))/(4-2)`.

`(a_(b)-a_(c) )/(b-c)` =
`((1)/(2)*(2)^(3) -(1)/(2)*(2)^(1))/(4-2)`.

`(a_(b)-a_(c) )/(b-c)` =
`(4-1)/(4-2)`.

`(a_(b)-a_(c) )/(b-c)` =
`(3)/(2)`.

Therefore,
`(3)/(2)`.

Answer 2

The rate of change between between n=2 and n=4 will be given as follows:
using points (4,4) and (2,1)
m=(4-1)/(4-2)
m=3/2

Answer: A] 3/2