What is the 105th term of the sequence:21, 17, 13, 9

The first thing we are going to to is checking if the sequence is arithmetic of geometric. A sequence is arithmetic if it has a common difference, [tex]d[/tex]. A sequence is geometric if it has a common ratio, [tex]r[/tex].
Lets test for a common difference first. To do that we are going to subtract the current term from the previous term:
[tex]9-13=-4[/tex]
[tex]13-17=-4[/tex]
[tex]17-21=-4[/tex]
Since we have a common difference, [tex]d=-4[/tex], or sequence is arithmetic. 
Now, to find its 105 term, we are going to find its explicit formula using the general form of an arithmetic sequence: [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 diference
We can infer for our sequence that [tex]a_{1}=21[/tex], and for previews calculations we know that [tex]d=-4[/tex]. So lets replace those values:
[tex]a_{n}=a_{1}+(n-1)d[/tex]
[tex]a_{n}=21+(n-1)(-4)[/tex]
[tex]a_{n}=21-4n+4[/tex]
[tex]a_{n}=25-4n[/tex]
Finally, to find the 105th term of the sequence, we just need to replace [tex]n[/tex] with 105 in our explicit formula:
[tex]a_{n}=25-4n[/tex]
[tex]a_{105}=25-4(105)[/tex]
[tex]a_{105}=25-420[/tex]
[tex]a_{105})=-395[/tex]

We can conclude that the 105th term of the sequence is -395.