Answer
$a_n=\sqrt3(n)$
$a_{10}= 10\sqrt3$
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 $a=\sqrt3$ and $d=\sqrt3$.
This means that the $n^{th}$ term of the sequence is given by the formula:
$a_n = \sqrt3 + \sqrt3(n-1)
\\a_n= \sqrt3[1+(n-1)]
\\a_n=\sqrt3(1+n-1)
\\a_n=\sqrt3(n)$
Thus, the 10th term of the sequence is:
$a_{10} = \sqrt3(10)
\\a_{10}= 10\sqrt3$
