Answer:
a_n = 2^(n - 1) 3^(3 - n)
Step-by-step explanation:
9,6,4,8/3,…
a1 = 3^2
a2 = 3 * 2
a3 = 2^2
As we can see, the 3 ^x is decreasing and the 2^ y is increasing
We need to play with the exponent in terms of n
Lets look at the exponent for the base of 2
a1 = 3^2 2^0
a2 = 3^1 2^1
a3 = 3^ 0 2^2
an = 3^ 2^(n-1)
I picked n-1 because that is where it starts 0
n = 1 (1-1) =0
n=2 (2-1) =1
n=3 (3-1) =2
Now we need to figure out the exponent for the 3 base
I will pick (3-n)
n =1 (3-1) =2
n =2 (3-2) =1
n=3 (3-3) =0
Using the recursion equation, it is found that the value of the 2nd iterate is:
![x_2 = 3.16228](https://tex.z-dn.net/?f=x_2%20%3D%203.16228)
<h3>What is the recursive equation?</h3>
The value of the nth iteration is given by:
![x_n = \frac{x_{n-1} + \frac{10}{x_{n-1}}}{2}](https://tex.z-dn.net/?f=x_n%20%3D%20%5Cfrac%7Bx_%7Bn-1%7D%20%2B%20%5Cfrac%7B10%7D%7Bx_%7Bn-1%7D%7D%7D%7B2%7D)
The initial estimate is:
![x_0 = 3.1](https://tex.z-dn.net/?f=x_0%20%3D%203.1)
Hence, the 1st iterate is given by:
![x_1 = \frac{x_0 + \frac{10}{x_0}}{2} = \frac{3.1 + \frac{10}{3.1}}{2} = 3.1629](https://tex.z-dn.net/?f=x_1%20%3D%20%5Cfrac%7Bx_0%20%2B%20%5Cfrac%7B10%7D%7Bx_0%7D%7D%7B2%7D%20%3D%20%5Cfrac%7B3.1%20%2B%20%5Cfrac%7B10%7D%7B3.1%7D%7D%7B2%7D%20%3D%203.1629)
The 2nd iterate is:
![x_2 = \frac{x_1 + \frac{10}{x_1}}{2} = \frac{3.1629 + \frac{10}{3.1629}}{2} = 3.16228](https://tex.z-dn.net/?f=x_2%20%3D%20%5Cfrac%7Bx_1%20%2B%20%5Cfrac%7B10%7D%7Bx_1%7D%7D%7B2%7D%20%3D%20%5Cfrac%7B3.1629%20%2B%20%5Cfrac%7B10%7D%7B3.1629%7D%7D%7B2%7D%20%3D%203.16228)
Thus, the fourth option is correct.
You can learn more about recursive equations at brainly.com/question/6561461
Answer:
pretty boring, I'm kind of tired to be honest. What ab you?
thanks for the points though