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, . A sequence is geometric if it has a common ratio, .
Lets test for a common difference first. To do that we are going to subtract the current term from the previous term:



Since we have a common difference, , 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: 
where
is the nth term
is the first term
is the position of the term in the sequence 
is the common diference
We can infer for our sequence that , and for previews calculations we know that . So lets replace those values:




Finally, to find the 105th term of the sequence, we just need to replace  with 105 in our explicit formula:





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

The answer of this question is 672 .

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