Answer:
The nth term of the geometric sequence is is 32805
Step-by-step explanation:
The nth term of a geometric sequence is given by
[tex]$ a_n = a_1 \cdot r^{n - 1} $[/tex]
Where [tex]a_1\\[/tex] is the first term and [tex]r[/tex] is the common ratio
We are given the fourth term of this sequence
[tex]a_4 = -135[/tex]
The common ratio is
[tex]r = -3[/tex]
Once we find the 1st term then we can find any other term.
[tex]a_4 = a_1 \cdot r^{4 - 1} \\\\a_4 = a_1 \cdot r^{3} \\\\-135 = a_1 \cdot (-3)^{3} \\\\-135 = a_1 \cdot (-27) \\\\a_1 = \frac{-135}{-27} \\\\a_1 = 5[/tex]
So the ninth term of this geometric sequence is
[tex]a_n = a_1 \cdot r^{n - 1} \\\\a_9 = a_1 \cdot r^{9 - 1} \\\\a_9 = a_1 \cdot r^{8} \\\\a_9 = 5 \cdot (-3)^{8} \\\\a_9 = 5 \cdot (6561) \\\\a_9 = 32805[/tex]
Therefore, the nth term of the geometric sequence is is 32805