Let the three numbers be x, y, and z.
If the sum of the three numbers is 3, then x+y+z=3
If subtracting the second number from the sum of the first and third numbers gives 9, then x+z-y=9
If subtracting the third number from the sum of the first and second numbers gives -5, then x+y-z=-5
This forms the system of equations:
[1] x+y+z=3
[2] x-y+z=9
[3] x+y-z=-5
First, to find y, let's take do [1]-[2]:
x+y+z=3
-x+y-z=-9
2y=-6
y=-3
Then, to find z, let's do [1]-[3]:
x+y+z=3
-x+-y+z=5
2z=8
z=4
Now that you have y and z, plug them into [1] to find x:
x+y+z=3
x-3+4=3
x=2
So the three numbers are 2,-3, and 4.
Answer:
![a_{n}=45-3n](https://tex.z-dn.net/?f=a_%7Bn%7D%3D45-3n)
Step-by-step explanation:
Method 1:
Arithmetic sequence is in the form
![a_{n} =a_{1} +(n-1)d\\](https://tex.z-dn.net/?f=a_%7Bn%7D%20%3Da_%7B1%7D%20%2B%28n-1%29d%5C%5C)
d is the common difference, can be found by:
![d=a_{n}-a_{n-1}=-3](https://tex.z-dn.net/?f=d%3Da_%7Bn%7D-a_%7Bn-1%7D%3D-3)
Subtituting the
and ![d](https://tex.z-dn.net/?f=d)
You get:
![a_{n}=42+(-3)(n-1)=45-3n](https://tex.z-dn.net/?f=a_%7Bn%7D%3D42%2B%28-3%29%28n-1%29%3D45-3n)
Method 2 (Mathematical induction):
Assume it is in form ![a_{n}=45-3n](https://tex.z-dn.net/?f=a_%7Bn%7D%3D45-3n)
Base step: ![a_{1} =45-3(1)=42](https://tex.z-dn.net/?f=a_%7B1%7D%20%3D45-3%281%29%3D42)
Inducive hypophesis: ![a_{n}=45-3n](https://tex.z-dn.net/?f=a_%7Bn%7D%3D45-3n)
GIven: ![a_{n+1} =a_{n}-3](https://tex.z-dn.net/?f=a_%7Bn%2B1%7D%20%3Da_%7Bn%7D-3)
![a_{n+1}=45-3n-3=45-3(n+1)](https://tex.z-dn.net/?f=a_%7Bn%2B1%7D%3D45-3n-3%3D45-3%28n%2B1%29)
Proved by mathematical induction
![a_{n}=45-3n](https://tex.z-dn.net/?f=a_%7Bn%7D%3D45-3n)
1.3y +3.2 = 1.3y +3.2
we notice that both sides of the equation are identical. So substitute y with any value and the equation would still be correct.
y has infinite solutions.
Answer:
The maximum will be 78
Step-by-step explanation: