Answer:
[tex]a_{n}=4+3(n-1)[/tex]
Step-by-step explanation:
The given recursive rule is
[tex]a_{1}=4\\a_{n}=a_{n-1}+3[/tex]
According to this recursive rule, the sequence is
[tex]4, 7, 10, 13, 16, 19,...[/tex]
Because, the recursive rule states that each new term must be 3 units greater.
Now, an explicit form of this sequence could be found using this formula
[tex]a_{n}=a_{1}+(n-1)d[/tex]
Where [tex]d=3[/tex] and [tex]a_{1}=4[/tex]
Replacing these values, we have
[tex]a_{n}=4+3(n-1)[/tex]
Therefore, the explict form is [tex]a_{n}=4+3(n-1)[/tex], which can be used to find any tem of the arithmetic sequence.
