Step-by-step explanation:
a vector multiplied by a scalar is equal to it's image. The expression above gives an equation and after solving, it gives you the image
5.5 quarts equals 22 cups. (There are 4cups in a quart, so 4 * 5.5 = 22)
22-4= 18 cups
Answer:
-5
Step-by-step explanation:
3 minus 8 equals -5
(20 characters needed)
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)