Answer
$a_n=-1 \cdot (-3)^{n-1}$
Work Step by Step
RECALL:
(1) 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
(2) The common ratio of a geometric sequence is equal to the quotient of any term and the term before it:
$r = \dfrac{a_n}{a_{n-1}}$
The given geometric sequence has:
$a_6=243$
$r=-3$
Note that:
$a_6=a_1 \cdot (r)^{6-1}
\\a_6=a_1 \cdot r^5$
Substitute the given values f $a_6$ and $r$ to obtain:
$a_6 = a_1 \cdot r^5
\\243=a_1 \cdot (-3)^5
\\243=a_1 \cdot (-243)
\\\dfrac{243}{-243} = a_1
\\-1=a_1$
Thus, the $n^{th}$ term of the sequence is given by the formula:
$a_n = a_1 \cdot r^{n-1}
\\a_n=-1 \cdot (-3)^{n-1}$
