Answer
$a_n=-2+4(n-1)$
$a_{51} = 198$
Work Step by Step
RECALL:
The $n^{th}$ term of an arithmetic sequence can be found using the formula:
$a_n = a_1 + (n-1)d$
where $a_1$ = first term and $d$ = common difference
The given sequence has:
$a_1=-2$;
$d=4$
Substitute these values into the formula for the $n^{th}$ term to obtain:
$a_n=a_1 + (n-1)d
\\a_n=-2+(n-1)(4)
\\a_n=-2+4(n-1)$
To find the 51st term, substitute $51$ for $n$ to obtain:
$a_{51} = -2+4(51-1)
\\a_{51}=-2+4(50)
\\a_{51} = -2+200
\\a_{51} = 198$
