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

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

Answer 2

Answer:

$\frac{3}{2}$.

Step-by-step explanation:

Given :$a_{n} = \frac{1}{2} * 2^{n-1}$

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

Solution : We have given that $a_{n} = \frac{1}{2} * 2^{n-1}$.

The average rate of change of $a_{n}$ on interval [b,c] =  that b =2 , c = 4 ,

Thus, $\frac{a_{b}-a_{c}}{b-c}$ = $\frac{\frac{1}{2}*(2)^{4-1} -\frac{1}{2}*(2)^{2-1}}{4-2}$.

$\frac{a_{b}-a_{c} }{b-c}$ = $\frac{\frac{1}{2}*(2)^{3} -\frac{1}{2}*(2)^{1}}{4-2}$.

$\frac{a_{b}-a_{c} }{b-c}$ = $\frac{4-1}{4-2}$.

$\frac{a_{b}-a_{c} }{b-c}$ = $\frac{3}{2}$.

Therefore,  $\frac{3}{2}$.