Answer:
Please check the explanation.
Step-by-step explanation:
Given the sequence
0.4, 0.8, 1.2, 1.6, ...
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
![0.8-0.4=0.4,\:\quad \:1.2-0.8=0.4,\:\quad \:1.6-1.2=0.4](https://tex.z-dn.net/?f=0.8-0.4%3D0.4%2C%5C%3A%5Cquad%20%5C%3A1.2-0.8%3D0.4%2C%5C%3A%5Cquad%20%5C%3A1.6-1.2%3D0.4)
The difference between all the adjacent terms is the same and equal to
![d=0.4](https://tex.z-dn.net/?f=d%3D0.4)
As the first element of the sequence is
![a_1=0.4](https://tex.z-dn.net/?f=a_1%3D0.4)
Thus, the relationship between the terms in each arithmetic sequence can be determined by using the formula
![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)
substituting
, and ![d=0.4](https://tex.z-dn.net/?f=d%3D0.4)
![a_n=0.4\left(n-1\right)+0.4](https://tex.z-dn.net/?f=a_n%3D0.4%5Cleft%28n-1%5Cright%29%2B0.4)
![a_n=0.4n](https://tex.z-dn.net/?f=a_n%3D0.4n)
Therefore, the relationship between the terms in each arithmetic sequence is:
Finding the next three terms:
Given the sequence
![a_n=0.4n](https://tex.z-dn.net/?f=a_n%3D0.4n)
putting n = 5 to determine the 5th term
![a_5=0.4\left(5\right)](https://tex.z-dn.net/?f=a_5%3D0.4%5Cleft%285%5Cright%29)
![a_5=2](https://tex.z-dn.net/?f=a_5%3D2)
putting n = 6 to determine the 6th term
![a_6=0.4\left(6\right)](https://tex.z-dn.net/?f=a_6%3D0.4%5Cleft%286%5Cright%29)
![a_6=2.4](https://tex.z-dn.net/?f=a_6%3D2.4)
putting n = 7 to determine the 7th term
![a_7=0.4\left(7\right)](https://tex.z-dn.net/?f=a_7%3D0.4%5Cleft%287%5Cright%29)
![a_7=2.8](https://tex.z-dn.net/?f=a_7%3D2.8)
Therefore, the next three terms are: