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>
9514 1404 393
Answer:
real, rational
Step-by-step explanation:
The ratio of two mutually prime natural numbers is not ...
irrational, integer, whole, natural
The ratio 5/6 is ...
real, rational
"Twice the dimensions" means the length, width, and height
of the new cube are all 6.
To build that cube, you need (6 x 6 x 6) = 216 blocks.
Answer:
x=80
Step-by-step explanation:
To find the average, we take the numbers, add them up. Then divide by the number of terms we added.
Let x= the unknown number
The average =90
Average = (138+40+102+x)/4
90 = (138+40+102+x)/4
Multiply by 4 on each side
90*4 =(138+40+102+x)/4 *4
360 = (138+40+102+x)
Combine like terms
360 = 280 +x
Subtract 280 from each side
360-280 = 280+x-280
80 =x