Answer:
Please check the explanation.
Step-by-step explanation:
Given the sequence
2, 6, 10, 14, 18
An arithmetic sequence has a constant difference and is defined as
![\:a_n=a_1+\left(n-1\right)d](https://tex.z-dn.net/?f=%5C%3Aa_n%3Da_1%2B%5Cleft%28n-1%5Cright%29d)
compute the differences of all the adjacent terms
![6-2=4,\:\quad \:10-6=4,\:\quad \:14-10=4,\:\quad \:18-14=4](https://tex.z-dn.net/?f=6-2%3D4%2C%5C%3A%5Cquad%20%5C%3A10-6%3D4%2C%5C%3A%5Cquad%20%5C%3A14-10%3D4%2C%5C%3A%5Cquad%20%5C%3A18-14%3D4)
The difference between all the adjacent terms is the same.
Thus,
![d=4](https://tex.z-dn.net/?f=d%3D4)
and
![a_1=2](https://tex.z-dn.net/?f=a_1%3D2)
Therefore, the nth term is computed by:
![a_n=4\left(n-1\right)+2](https://tex.z-dn.net/?f=a_n%3D4%5Cleft%28n-1%5Cright%29%2B2)
![a_n=4n-2](https://tex.z-dn.net/?f=a_n%3D4n-2)
Thus, position to term rule of 2, 6, 10, 14, 18 multiply by __4___ and subtract by __2__.
The equation would be:
x - 9 < 4
Simplify (add 9)
Solution: x < 13
Answer:
11.18 miles
Step-by-step explanation:
The sides of a right triangle a, b, c are related by the equation
a^2 + b^2 = c^2
where c is the longest side of the triangle
Hence given that A connects B and C directly and forms a right angle at A
5^2 + 10^2 = c^2
Where c is the length of the road
25 + 100 = c^2
125 = c^2
c = 125^1/2
= 11.18 miles