Remember that the explicit formula for an arithmetic sequence is:
[tex]a_{n}=a_{1}+(n-1)d[/tex]
where
[tex]a_{n}[/tex] is the nth term
[tex]a_{1}[/tex] is the first term
[tex]n[/tex] is the position of the term in the sequence
[tex]d[/tex] is the common difference
We know from our problem that [tex]a_{1}=7[/tex] and [tex]d=7[/tex], so lets replace those vales in our formula:
[tex]a_{n}=7+(n-1)7[/tex]
[tex]a_{n}=7+7n-7[/tex]
[tex]a_{n}=7n[/tex]
Now that we have the explicit formula for our sequence we can find its first 5 terms:
[tex]a_{1}=7[/tex]
[tex]a_{2}=7(2)=14[/tex]
[tex]a_{3}=7(3)=21[/tex]
[tex]a_{4}=7(4)=28[/tex]
[tex]a_{5}=7(5)=35[/tex]
We can conclude that the first five terms of our arithmetic are: 7,14,21,28,35, and its explicit formula is [tex]a_{n}=7n[/tex]
