Given the points A and B
The coordinates of point A = ( 3 , 1 )
The coordinates of point B = (-1 , -1)
The midpoint of AB, is the point C
C will be calculated as following :
![C=\frac{A+B}{2}=\frac{(3,1)+(-1,-1)}{2}=\frac{(3-1,1-1)}{2}=\frac{(2,0)}{2}=(1,0)](https://tex.z-dn.net/?f=C%3D%5Cfrac%7BA%2BB%7D%7B2%7D%3D%5Cfrac%7B%283%2C1%29%2B%28-1%2C-1%29%7D%7B2%7D%3D%5Cfrac%7B%283-1%2C1-1%29%7D%7B2%7D%3D%5Cfrac%7B%282%2C0%29%7D%7B2%7D%3D%281%2C0%29)
so, the midpoint of AB = (1 , 0 )
Literally just learned this in algebra are you a freshman too ????? lol
A natural number is a positive or nonnegative integer. All the counting numbers, (1, 2, 3, etc.) are natural numbers. Other names for the same type of object include whole number and counting counting.
For the given geometric sequence, we have:
![a_1 = 9\\\\a_n = (-1/3)*a_{n-1}](https://tex.z-dn.net/?f=a_1%20%3D%209%5C%5C%5C%5Ca_n%20%3D%20%28-1%2F3%29%2Aa_%7Bn-1%7D)
So the correct option is B.
<h3>
Which is the recursive formula?</h3>
Here we have the geometric sequence:
![a_n = 9*(-\frac{1}{3} )^{(n - 1)}](https://tex.z-dn.net/?f=a_n%20%3D%209%2A%28-%5Cfrac%7B1%7D%7B3%7D%20%29%5E%7B%28n%20-%201%29%7D)
To get the initial value of the geometric sequence, we just need to replace n by 1, so we get:
![a_1 = 9*(-\frac{1}{3} )*(1 - 1) = 9](https://tex.z-dn.net/?f=a_1%20%3D%209%2A%28-%5Cfrac%7B1%7D%7B3%7D%20%29%2A%281%20-%201%29%20%3D%209)
Now, notice that the common ratio is (-1/3), this means that each term of the sequence is (-1/3) times the previous term.
![a_n = (-1/3)*a_{n-1}](https://tex.z-dn.net/?f=a_n%20%3D%20%28-1%2F3%29%2Aa_%7Bn-1%7D)
Then the correct option is B.
If you want to learn more about geometric sequences:
brainly.com/question/1509142
#SPJ1
Getting the percentage increase, we can form the formula or equation.
Percentage increase = ($1.00 - $0.40) / $0.40 * 100
<span>Percentage increase = ($0.60) / $0.40 * 100
</span><span>Percentage increase = 1.5 * 100
</span><span>Percentage increase = 150%
</span>
So there is a 150% increase from the original price.
The answer is 225 im just guessing