Answer
$a_n= \frac{5}{2}-\frac{1}{2}(n-1)$
$a_{10}=2$
Work Step by Step
RECALL:
The $n^{th}$ term $a_n$ of an arithmetic sequence can be found using the formula:
$a_n = a + d(n-1)$
where
$a$ = first term
$d$ = common difference
$n$ = term number
The given arithmetic sequence has $a=\frac{5}{2}$ and $d=-\frac{1}{2}$.
This means that the $n^{th}$ term of the sequence is given by the formula:
$a_n = \frac{5}{2} + (-\frac{1}{2})(n-1)
\\a_n= \frac{5}{2}-\frac{1}{2}(n-1)$
Thus, the 10th term of the sequence is:
$a_{10} = \frac{5}{2}-\frac{1}{2}(10-1)
\\a_{10}= \frac{5}{2} - \frac{1}{2}(9)
\\a_{10} = \frac{5}{2} - \frac{9}{2}
\\a_{10} = \frac{5-9}{2}
\\a_{10}= -\frac{4}{2}
\\a_{10}=2$
