Answer
$a_5=162$
$a_n=2 \cdot 3^{n-1}$
Work Step by Step
RECALL:
The $n^{th}$ term $a_n$ of a geometric sequence is given by the formula:
$a_n=a_1 \cdot r^{n-1}$
where
$a_1$ = first term
$r$ = common ratio
The given geometric sequence has:
$a_1=2$
$r=3$
Thus, the $n^{th}$ term of the sequence is given by the formula:
$a_n = 2 \cdot 3^{n-1}$
The 5th term can be found by substituting $5$ for $n$:
$a_5=2 \cdot 3^{5-1}
\\a_5=2 \cdot 3^4
\\a_5 = 2(81)
\\a_5 = 162$