Answer:
6561/256
Step-by-step explanation:
You can notice that each term is equal to the previous term multiplied by 3/2. This means that it is a geometric series. The formula to find the nth term is as follows:
[tex]a_{n}= a_{1} *(r)^{n-1}[/tex]
The first term, a1, is 1 and r, the common ratio is 3/2 because that is what you are multiplying by. We can also substitute in n as 9 because we are looking for the ninth term:
[tex]a_{9} = 1 *(\frac{3}{2} )^{9-1}\\\\a_{9} = (\frac{3}{2})^{8}\\\\a_{9} =\frac{3^8}{2^8} \\\\a_{9} =\frac{6561}{256}[/tex]
