Answer
$a_n=-2+4(n-1)$
and $a_{51} =198$
Work Step by Step
The $n^{th}$ term of an arithmetic sequence is given by the formula:
$a_n = a_1 + (n-1)d (1)$
where
$a_1 = \ First \ Term; \\ d = \ Common \ Difference$
We have: $a_1=-2 \\ d=4$
Next, we will substitute the above data into the formula (1) to obtain:
$a_n=-2+(4)(n-1) \implies a_n=-2+4(n-1)$
In order to compute the $51st$ term, we need to plug in $51$ for $n$ into the above form to obtain:
$a_{51} = -2+4(51-1) =-2+200$
So, $a_{51} =198$