Answer
$a_n=6-2(n-1)$
$a_{51} = -94$
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:
$a_1=6$;
$d=-2$
Substitute these values into the formula for the $n^{th}$ term to obtain:
$a_n=a_1 + (n-1)d
\\a_n=6+(n-1)(-2)
\\a_n=6+(-2)(n-1)
\\a_n=6-2(n-1)$
To find the 51st term, substitute $51$ for $n$ to obtain:
$a_{51} = 6-2(51-1)
\\a_{51}=6-2(50)
\\a_{51} =6-100
\\a_{51} = -94$
