So you are working on the possible answers.

You are not supposed to do that. The given 4 possible answers are just for checking your work on the problem.

In an Arithmetic sequence, there is common difference, d, between successive terms. So a2 = a1 +d; a3 = a2 +d; a99 = a98 +d; ......

where a1 means 1st term, a2 = 2nd term, a99 = 99th term, ....

7, 12, 17, 22,...

Meaning, a1 = 7, a2 = 12; a3 = 17; a4 = 22

So, d = a2 -a1 = 12 -7 = 5

Or, d = a3 -a2 = 17 -12 = 5

Or, d = a4 -a3 = 22 -17 = 5

So d is really 5.

Now, a2 = a1 +d

a3 = a2 +d = (a1 +d) +d = a1 +2d ----------------> a1 +(3-1)d

a4 = a3 +d = (a1 +2d) +d = a1 +3d ---------------> a1 +(4-1)d

So,

an = a1 +(n-1)d -----***

Plugging the a1=7 and d=5 in,

an = 7 +(n-1)(5)

an = 7 +5n -5

an = 5n +2 ----------------answer.