Answer:
The function which represents this sequence will be:
![a_n=-15n+110](https://tex.z-dn.net/?f=a_n%3D-15n%2B110)
Hence, option (A) is true.
Step-by-step explanation:
Given the sequence
![95, 80, 65, 50, ...](https://tex.z-dn.net/?f=95%2C%2080%2C%2065%2C%2050%2C%20...)
An arithmetic sequence has a constant difference 'd' and is defined by
![a_n=a_1+\left(n-1\right)d](https://tex.z-dn.net/?f=a_n%3Da_1%2B%5Cleft%28n-1%5Cright%29d)
computing the differences of all the adjacent terms
![80-95=-15,\:\quad \:65-80=-15,\:\quad \:50-65=-15](https://tex.z-dn.net/?f=80-95%3D-15%2C%5C%3A%5Cquad%20%5C%3A65-80%3D-15%2C%5C%3A%5Cquad%20%5C%3A50-65%3D-15)
As the difference is the same, so
![d = -15](https://tex.z-dn.net/?f=d%20%3D%20-15)
as
![a_1=95](https://tex.z-dn.net/?f=a_1%3D95)
Thus, substituting
,
in the nth term of an arithmetic sequence
![a_n=a_1+\left(n-1\right)d](https://tex.z-dn.net/?f=a_n%3Da_1%2B%5Cleft%28n-1%5Cright%29d)
![a_n=-15\left(n-1\right)+95](https://tex.z-dn.net/?f=a_n%3D-15%5Cleft%28n-1%5Cright%29%2B95)
![a_n=-15n+110](https://tex.z-dn.net/?f=a_n%3D-15n%2B110)
Therefore, the function which represents this sequence will be:
![a_n=-15n+110](https://tex.z-dn.net/?f=a_n%3D-15n%2B110)
Hence, option (A) is true.
Step-by-step explanation:
12a = 13a - a
12a = 14a - 2a
12a = 15a - 3a
12a = 16a - 4a
12a = 17a - 5a
...
Answer:
15
Step-by-step explanation:
![3x-15=4x \\ \\ x-15=0 \\ \\ x=15](https://tex.z-dn.net/?f=3x-15%3D4x%20%5C%5C%20%5C%5C%20x-15%3D0%20%5C%5C%20%5C%5C%20x%3D15)
So either a and d or a and c :)