Answer
$a_n=(-1)(-3)^{n-1}$
Work Step by Step
The $n^{th}$ term of a geometric sequence is given by the formula:
$ a_n=a_1r^{n-1}$
where $r$=common ratio and $a_1$= the first term
The common ratio of a geometric sequence is equal to the quotient (ratio) of any term and the term before it:
$ \ r = \dfrac{a_n}{a_{n-1}}$ or, $r=\dfrac{a_2}{a_1}$
Here, we have: $a_6= 243$ and $r=-3$
So, $a_6=a_1r^{6-1}=243 ; \\ a_1(-3)^{5}=243 ; \\ a_1=-1$
Therefore, the $n^{th}$ term of the given sequence is given by the formula:
$ a_n=a_1r^{n-1} ; \\ a_n=(-1)(-3)^{n-1}$
