First we need to find what kind of sequence we have. To do that we are going to test if the sequence as a difference
![d](https://tex.z-dn.net/?f=d)
, in which case it will be an arithmetic sequence, or a ratio
![r](https://tex.z-dn.net/?f=r)
, in which case it will be geometric sequence.
The formula to find
![d](https://tex.z-dn.net/?f=d)
is
![d=a_{n}-a_{n-a}](https://tex.z-dn.net/?f=d%3Da_%7Bn%7D-a_%7Bn-a%7D)
where
![a_{n}](https://tex.z-dn.net/?f=a_%7Bn%7D)
is the current term in the sequence
![a_{n-1}](https://tex.z-dn.net/?f=a_%7Bn-1%7D)
is the previous term in the sequence
The formula to find
![r](https://tex.z-dn.net/?f=r)
is
![r= \frac{a _{n} }{a _{n-1} }](https://tex.z-dn.net/?f=r%3D%20%5Cfrac%7Ba%20_%7Bn%7D%20%7D%7Ba%20_%7Bn-1%7D%20%7D%20)
where
![a_{n}](https://tex.z-dn.net/?f=a_%7Bn%7D)
is the current term in the sequence
![a_{n-1}](https://tex.z-dn.net/?f=a_%7Bn-1%7D)
is the previous term in the sequence
- For
![a_{n}=10](https://tex.z-dn.net/?f=a_%7Bn%7D%3D10)
and
![r= \frac{10}{7}](https://tex.z-dn.net/?f=r%3D%20%5Cfrac%7B10%7D%7B7%7D%20)
- For
![a_{n}=4](https://tex.z-dn.net/?f=a_%7Bn%7D%3D4)
and
![a_{n-1}=1](https://tex.z-dn.net/?f=a_%7Bn-1%7D%3D1)
:
![r=4](https://tex.z-dn.net/?f=r%3D4)
Since
![d](https://tex.z-dn.net/?f=d)
is equal in both procedures whereas
![r](https://tex.z-dn.net/?f=r)
is not, we can conclude that our sequence is an arithmetic sequence.
Now we are going to use the explicit formula of an arithmetic sequence
![a_{n}=a_{1}+(n-1)d](https://tex.z-dn.net/?f=a_%7Bn%7D%3Da_%7B1%7D%2B%28n-1%29d)
where
![a_{n}](https://tex.z-dn.net/?f=a_%7Bn%7D)
is the nth term
![a_{1}](https://tex.z-dn.net/?f=a_%7B1%7D)
is the first term
![n](https://tex.z-dn.net/?f=n)
is the position of the term in the sequence
![d](https://tex.z-dn.net/?f=d)
is the difference
We know that
![a_{1}=-2](https://tex.z-dn.net/?f=a_%7B1%7D%3D-2)
and
![d=3](https://tex.z-dn.net/?f=d%3D3)
, so lets replace those values in our formula:
![a_{n}=-2+(n-1)(3)](https://tex.z-dn.net/?f=a_%7Bn%7D%3D-2%2B%28n-1%29%283%29)
![a_{n}=-2+3n-3](https://tex.z-dn.net/?f=a_%7Bn%7D%3D-2%2B3n-3)
![a_{n}=3n-5](https://tex.z-dn.net/?f=a_%7Bn%7D%3D3n-5)
We can conclude that the correct answer is <span>
D) an = 3n - 5</span>
This can be solve by 3 variable equation
let x be the money of luke
y money of rachel
z money of daniel
first equation
x = y + 21
second equation
x = z + 48
third equation
x + y + z = 168
solving simultaneously
x =79
y = 58
z = 31
Answer:
3.636478334
Step-by-step explanation:
Hope This Helps!
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- Innverted
Answer:
omg sameeee
Step-by-step explanation:
lol