Answer:
![a_n= 4(-5)^{(n-1)}](https://tex.z-dn.net/?f=a_n%3D%204%28-5%29%5E%7B%28n-1%29%7D)
-10416
Step-by-step explanation:
a = 4
r = -5
geometric series: ![a_n=ar^{(n-1)} = 4(-5)^{(n-1)}](https://tex.z-dn.net/?f=a_n%3Dar%5E%7B%28n-1%29%7D%20%3D%204%28-5%29%5E%7B%28n-1%29%7D)
Determine which term = -12500:
![a_n=-12500](https://tex.z-dn.net/?f=a_n%3D-12500)
![4(-5)^{(n-1)}=-12500](https://tex.z-dn.net/?f=4%28-5%29%5E%7B%28n-1%29%7D%3D-12500)
![(-5)^{(n-1)} = -3125](https://tex.z-dn.net/?f=%28-5%29%5E%7B%28n-1%29%7D%20%3D%20-3125)
![(5)^{(n-1)} = 3125](https://tex.z-dn.net/?f=%285%29%5E%7B%28n-1%29%7D%20%3D%203125)
![(n-1)ln(5) = ln(3125)](https://tex.z-dn.net/?f=%28n-1%29ln%285%29%20%3D%20ln%283125%29)
![n-1 = ln(3125)/ln(5) = 5](https://tex.z-dn.net/?f=n-1%20%3D%20ln%283125%29%2Fln%285%29%20%3D%205)
![n = 5 + 1 = 6](https://tex.z-dn.net/?f=n%20%3D%205%20%2B%201%20%3D%206)
![a_6=-12500](https://tex.z-dn.net/?f=a_6%3D-12500)
Using geometric sum series formula: ![S_n=\frac{a(1-r^n)}{1-r}](https://tex.z-dn.net/?f=S_n%3D%5Cfrac%7Ba%281-r%5En%29%7D%7B1-r%7D)
Therefore, ![S_6=\frac{4(1-(-5)^6)}{1-(-5)} =\frac{-62496}{6} =-10416](https://tex.z-dn.net/?f=S_6%3D%5Cfrac%7B4%281-%28-5%29%5E6%29%7D%7B1-%28-5%29%7D%20%3D%5Cfrac%7B-62496%7D%7B6%7D%20%3D-10416)
Answer:
3/20
Step-by-step explanation:
She chose 3 songs out of twenty so those three songs should be out of that twenty.
Answer:
104°
Step-by-step explanation:
The straight line for
forms an angle of 180°
Therefore,
![x+y=180](https://tex.z-dn.net/?f=x%2By%3D180)
![x+76=180](https://tex.z-dn.net/?f=x%2B76%3D180)
![x=180-76](https://tex.z-dn.net/?f=x%3D180-76)
![x=104](https://tex.z-dn.net/?f=x%3D104)
Hey there!
Assuming you meant
![5r^2 - 12 = 68](https://tex.z-dn.net/?f=%205r%5E2%20-%2012%20%3D%2068%20%20)
If so, follow these steps so it can be a little bit easier to solve
Firstly, we have to
by
on each of your sides
![5r^2 -12 +12 \\ \\ 68 + 12](https://tex.z-dn.net/?f=%205r%5E2%20-12%20%2B12%20%5C%5C%20%5C%5C%2068%20%2B%2012%20%20)
![5r^2 = 5r^2 \\ \\ 68 + 12 = 80](https://tex.z-dn.net/?f=%205r%5E2%20%3D%205r%5E2%20%5C%5C%20%5C%5C%2068%20%2B%2012%20%3D%2080%20%20)
We get: ![5r^2 =80](https://tex.z-dn.net/?f=%205r%5E2%20%3D80%20%20)
Now, we have
by
on each of your sides
![\frac{5r^2}{5} = \frac{80}{5}](https://tex.z-dn.net/?f=%20%5Cfrac%7B5r%5E2%7D%7B5%7D%20%3D%20%5Cfrac%7B80%7D%7B5%7D%20%20)
![\frac{80}{5} = 16](https://tex.z-dn.net/?f=%20%5Cfrac%7B80%7D%7B5%7D%20%20%3D%2016%20%20)
We get: ![r^2 = 16](https://tex.z-dn.net/?f=%20r%5E2%20%3D%2016%20%20)
± ![\sqrt{16}](https://tex.z-dn.net/?f=%20%5Csqrt%7B16%7D%20%20)
Therefore , your answer is:
±![4](https://tex.z-dn.net/?f=%204%20%20)
Good luck on your assignment and enjoy your day!
~![LoveYourselfFirst:)](https://tex.z-dn.net/?f=%20LoveYourselfFirst%3A%29%20)