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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
[tex]a_n=a_1+\left(n-1\right)d[/tex]
Computing the differences of all the adjacent terms
[tex]0.8-0.4=0.4,\:\quad \:1.2-0.8=0.4,\:\quad \:1.6-1.2=0.4[/tex]
The difference between all the adjacent terms is the same and equal to
[tex]d=0.4[/tex]
As the first element of the sequence is
[tex]a_1=0.4[/tex]
Thus, the relationship between the terms in each arithmetic sequence can be determined by using the formula
[tex]a_n=a_1+\left(n-1\right)d[/tex]
substituting [tex]a_1=0.4[/tex], and [tex]d=0.4[/tex]
[tex]a_n=0.4\left(n-1\right)+0.4[/tex]
[tex]a_n=0.4n[/tex]
Therefore, the relationship between the terms in each arithmetic sequence is:
Finding the next three terms:
Given the sequence
[tex]a_n=0.4n[/tex]
putting n = 5 to determine the 5th term
[tex]a_5=0.4\left(5\right)[/tex]
[tex]a_5=2[/tex]
putting n = 6 to determine the 6th term
[tex]a_6=0.4\left(6\right)[/tex]
[tex]a_6=2.4[/tex]
putting n = 7 to determine the 7th term
[tex]a_7=0.4\left(7\right)[/tex]
[tex]a_7=2.8[/tex]
Therefore, the next three terms are: