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>
Answer:
n = 2p
Step-by-step explanation:
14n + 6p – 8n = 18p
Combine like terms
14n-8n +6p = 18p
6n +6p = 18p
Subtract 6p from each side
6n+6p -6p = 18p-6p
6n = 12p
Divide by 6
6n/6 = 12p/6
n = 2p
Length=width+x
l=w+x (x being the amount of feet longer than the width)
The first is one hundred thousand
the second is ten thousand
the third is one thousand
the fourth is one hundred
the fifth is ten
the sixth is one