Answer
$a_{n}=4n-3, \quad n=1,2,3...$
Work Step by Step
The differences between terms are $4,4,4,4,...$
This is constant, similar to the sequence of natural numbers:
$1,2,3,4,...$ where the difference between terms is $1$.
If we multiply each term of $1,2,3,4,...$ with $4$, we get
$4,8,12,16,20,24,...$
The difference between terms is now $4$, as in the problem.
We find a relationship between this sequence and the one given by the problem by observing the pattern:
$ 1=4-3\quad$ = $4n-3$ when $n=1,$
$ 5=8-3\quad$ = $4n-3$ when $n=2,$
$ 9=12-3\quad$ = $4n-3$ when $n=3,$
$ 13=16-3\quad$ = $4n-3$ when $n=4$
$ 17=20-3\quad$ = $4n-3$ when $n=5$
$...$
$a_{n}=4n-3, \quad n=1,2,3...$
