Answer
$a_{80}=\frac{83}{2}$
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:
$a_1=2$;
$d=\frac{5}{2} - 2 = \frac{5}{2} - \frac{4}{2} = \frac{1}{2}$
Substitute these values into the formula for the $n^{th}$ term to obtain:
$a_n=a_1 + (n-1)d
\\a_n=2+(n-1)(\frac{1}{2})
\\a_n=2+\frac{1}{2}(n-1)$
To find the 80th term, substitute $80$ for $n$ to obtain:
$a_{80} = 2+\frac{1}{2}(80-1)
\\a_{80}=2+\frac{1}{2}(79)
\\a_{80}=2+\frac{79}{2}
\\a_{80} =\frac{4}{2}+\frac{79}{2}
\\a_{80}=\frac{83}{2}$
