Answer:
12
Step-by-step explanation:
The given geometric series is
![\sum_{n = 1}^{ \infty} 12( { - \frac{1}{9} })^{n - 1}](https://tex.z-dn.net/?f=%20%5Csum_%7Bn%20%3D%201%7D%5E%7B%20%5Cinfty%7D%2012%28%20%7B%20-%20%20%5Cfrac%7B1%7D%7B9%7D%20%7D%29%5E%7Bn%20-%201%7D%20)
We want to determine the first term of this geometric series.
Recall that the explicit formula is
![a_{n} = 12( { - \frac{1}{9} })^{n - 1}](https://tex.z-dn.net/?f=%20a_%7Bn%7D%20%3D%2012%28%20%7B%20-%20%20%5Cfrac%7B1%7D%7B9%7D%20%7D%29%5E%7Bn%20-%201%7D%20)
To find the first term, we put n=1 to get:
![a_{1} = 12( { - \frac{1}{9} })^{1 - 1}](https://tex.z-dn.net/?f=a_%7B1%7D%20%3D%2012%28%20%7B%20-%20%20%5Cfrac%7B1%7D%7B9%7D%20%7D%29%5E%7B1%20-%201%7D%20)
This gives us:
![a_{1} = 12( { - \frac{1}{9} })^{0}](https://tex.z-dn.net/?f=a_%7B1%7D%20%3D%2012%28%20%7B%20-%20%20%5Cfrac%7B1%7D%7B9%7D%20%7D%29%5E%7B0%7D)
![a_{1} = 12(1) = 12](https://tex.z-dn.net/?f=a_%7B1%7D%20%3D%2012%281%29%20%3D%2012)
Therefore the first term is 12
Answer:
y=50
x=30
z=100
Step-by-step explanation:
x+20=y
2y=z
x+y+z=180
x+y+2y=180
3y+x=180
-y+x=-20
4y=200
y=50
x=30
z=100
Answer:
c and d
Step-by-step explanation:
i think
1/8 is half of 1/4
Step-by-step explanation:
1/8 + 1/8 = 1/4