Since the first 4 terms of the sequence are
9, 13, 17, 21
Since the difference between each 2 conescutive terms is
13 - 9 = 4
17 - 13 = 4
21 - 17 = 4
Then the constant difference is 4
Since the rule of the nth term is
[tex]a_n=a_1+(n-1)d[/tex]Since the first term is 9, then
a1 = 9
Since d is the constant difference, then
d = 4
Substitute them in the rule above
[tex]\begin{gathered} a_n=9+(n-1)4 \\ a_n=9+4n-4 \end{gathered}[/tex]Add the like terms
[tex]a_n=5+4n[/tex]The answer is
[tex]a_n=5+4n[/tex]