## College Algebra (10th Edition)

$a_n=6-2(n-1)$ $a_{51} = -94$
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: $a_{51} = 6-2(51-1) \\a_{51}=6-2(50) \\a_{51} =6-100 \\a_{51} = -94$