Describe the relationship between the terms in each arithmetic sequence. Then write the next three terms in the sequence. 0.4, 0.8, 1.2, 1.6, ...

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

Computing the differences of all the adjacent terms

The difference between all the adjacent terms is the same and equal to

As the first element of the sequence is

Thus, the relationship between the terms in each arithmetic sequence can be determined by using the formula

substituting , and

Therefore, the relationship between the terms in each arithmetic sequence is:

Finding the next three terms:

Given the sequence

putting n = 5 to determine the 5th term

putting n = 6 to determine the 6th term

putting n = 7 to determine the 7th term

Therefore, the next three terms are: