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

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

Explanation:

The given sequence is defined as

`a_n=1(3)^(n-1)`

The average rate of change from x₁ and x₂ is

`m=(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=(a_3-a_1)/(3-1)=(9-1)/(2)=(8)/(2)=4`

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