Answer: The 9th term is 6561
Step-by-step explanation:
The geometric sequences have the following formula
[tex]a_n = a_1(r)^{n-1}[/tex]
Where [tex]a_1[/tex] is the first term of the sequence and r is the common ratio between the consecutive terms of the sequence
In this case the sequence is 1 -3 9 -27
So [tex]a_1 = 1[/tex]
Observe that the common ratio r is:
[tex]r=\frac{-3}{1}=\frac{9}{3}=\frac{-27}{9}=-3[/tex]
So the formula is:
[tex]a_n = (-3)^{n-1}[/tex]
We want to find [tex]a_9[/tex]
[tex]a_9 = (-3)^{9-1}[/tex]
[tex]a_9 = (-3)^{8}=6561[/tex]
