Answer
$a_{n}=2(2n-1), \quad n=1,2,3...$
Work Step by Step
The differences between terms are 2,2,2,2,...
These are 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 2, we get
$2,4,6,8,10,...$
The difference between terms is now $2$, as in the problem.
We find a relationship between this sequence and the one given by the problem by observing the pattern:
$ 2=2+0\quad$ = $2n+2(n-1)=4n-2$ when n=$1,$
$ 6=4+2\quad$ = $2n+2(n-1)=4n-2$ when n=$2,$
$ 10=6+4\quad$ = $2n+2(n-1)=4n-2$ when n=$3,$
$ 14=8+6\quad$ = $2n+2(n-1)=4n-2$ when n=$4$
$ 18=10+8\quad$ = $2n+2(n-1)=4n-2$ when n=$5$
$...$
$a_{n}=4n-2=2(2n-1), \quad n=1,2,3...$
$a_{n}=2(2n-1), \quad n=1,2,3...$
