Question

The sequence an = 1(3)^(n − 1) is graphed below:


Find the average rate of change between n = 1 and n = 3.



A)1/3


B) 1


C) 3


D) 4

Answer 1

a(1)=(1)(3)^(1-1)
a(1)=1
a(3)=1(3)(3-1)=1(9)=9
rate=(9-1)/(3-1)=8/2=4 is average rate

Answer 2

Answer:

The correct option is D. The average rate of change between n = 1 and n = 3 is 4.

Step-by-step explanation:

The given sequence is defined as

$a_n=1(3)^{n-1}$

The average rate of change from x₁ and x₂ is

$m=\frac{f(x_2)-f(x_1)}{x_2-x_1}$

At x=1,

$a_1=1(3)^{1-1}=1$

At x=3,

$a_3=1(3)^{3-1}=9$

The average rate of change between n = 1 and n = 3.

$m=\frac{a_3-a_1}{3-1}=\frac{9-1}{2}=\frac{8}{2}=4$

The average rate of change between n = 1 and n = 3 is 4. Therefore option D is correct.