Answer
$a_{80} =-390$
Work Step by Step
RECALL:
(1) 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
(2) The common difference $d$ can be found by subtracting any term to the next term of the sequence:
$d=a_n - a_{n-1}$
The given sequence has:
$a_1=5$;
$d=0-5=-5$
Substitute these values into the formula for the $n^{th}$ term to obtain:
$a_n=a_1 + (n-1)d
\\a_n=5+(n-1)(-5)
\\a_n=5+(-5)(n-1)
\\a_n=5-5(n-1)$
To find the 80th term, substitute $80$ for $n$ to obtain:
$a_{80} = 5-5(80-1)
\\a_{80}=5-5(79)
\\a_{80}=5-395
\\a_{80} =-390$
