Answer:
![a_{n} = 32(\frac{1}{4})^{n-1}](https://tex.z-dn.net/?f=a_%7Bn%7D%20%3D%2032%28%5Cfrac%7B1%7D%7B4%7D%29%5E%7Bn-1%7D)
Step-by-step explanation:
The nth term of a geometric sequence is given by the following equation.
![a_{n+1} = ra_{n}](https://tex.z-dn.net/?f=a_%7Bn%2B1%7D%20%3D%20ra_%7Bn%7D)
In which r is the common ratio.
This can be expanded for the nth term in the following way:
![a_{n} = a_{1}r^{n-1}](https://tex.z-dn.net/?f=a_%7Bn%7D%20%3D%20a_%7B1%7Dr%5E%7Bn-1%7D)
In which
is the first term.
This means that for example:
![a_{3} = a_{1}r^{3-1}](https://tex.z-dn.net/?f=a_%7B3%7D%20%3D%20a_%7B1%7Dr%5E%7B3-1%7D)
So
![a_{3} = a_{1}r^{2}](https://tex.z-dn.net/?f=a_%7B3%7D%20%3D%20a_%7B1%7Dr%5E%7B2%7D)
![2 = a_{1}(\frac{1}{4})^{2}](https://tex.z-dn.net/?f=2%20%3D%20a_%7B1%7D%28%5Cfrac%7B1%7D%7B4%7D%29%5E%7B2%7D)
![2 = \frac{a_{1}}{16}](https://tex.z-dn.net/?f=2%20%3D%20%5Cfrac%7Ba_%7B1%7D%7D%7B16%7D)
![a_{1} = 32](https://tex.z-dn.net/?f=a_%7B1%7D%20%3D%2032)
Then
![a_{n} = 32(\frac{1}{4})^{n-1}](https://tex.z-dn.net/?f=a_%7Bn%7D%20%3D%2032%28%5Cfrac%7B1%7D%7B4%7D%29%5E%7Bn-1%7D)
Answer:
$36
Step-by-step explanation:
22+14=36
Answer:
45 eggs left
Step-by-step explanation:
if they had 4 crates and each crate has 18, then we have a total of 72 eggs
subtract 27 eaten eggs from 72
72-27=45
they have 45 eggs left
Answer:
A) ![$ \frac{1}{5} $](https://tex.z-dn.net/?f=%24%20%5Cfrac%7B1%7D%7B5%7D%20%24)
B) - 5
C) Not Possible
D) 5
E) ![$ \frac{-1}{5} $](https://tex.z-dn.net/?f=%24%20%5Cfrac%7B-1%7D%7B5%7D%20%24)
- Step-by-step explanation:
- All integers are rational numbers. But not all rational numbers are integers.
- All whole numbers are integers. But not all integers are whole numbers.
I am a rational number but not an integer. Located on the right of 0.
This means that it should be a positive number. Since, it is a rational number but not an integer, it should be of the form
.
From, the options
would fit this description.
I am a rational number and an integer but not a whole number.
This means that it should be a negative integer. Since, all positive integers and zero would be whole numbers. From the options, the answer would be -5.
I am a whole number but not an integer.
This is clearly not possible because all whole numbers are a subset of integers.
I am a rational number, a whole number and an integer.
This means it is a positive integer. 5 would fit this description.
I am a rational number but not an integer; located on the left side of 0.
This means it is a negative number.
should be the answer.
Mathematics is math, geometry, algebra, calculus