Find the nth term for the geometric sequence with the given values. \[ a_{4}=45, r=\frac{1}{3}, n=9 \] The 9 th term of the sequence is $\square$ (Simplify your answer.)

Step 1 ：We are given the 4th term of the geometric sequence, \(a_4 = 45\), the common ratio, \(r = \frac{1}{3}\), and we are asked to find the 9th term, \(a_9\).

Step 2 ：The nth term of a geometric sequence can be found using the formula: \(a_n = a_1 * r^{(n-1)}\). However, we are given \(a_4\) instead of \(a_1\).

Step 3 ：We can find \(a_1\) by rearranging the formula: \(a_1 = \frac{a_4}{r^{(4-1)}}\).

Step 4 ：Substituting the given values into the formula, we get \(a_1 = \frac{45}{(\frac{1}{3})^{(4-1)}} = 1215\).

Step 5 ：Now that we have the first term, \(a_1 = 1215\), we can substitute it back into the original formula to find the 9th term, \(a_9\).

Step 6 ：Substituting the values into the formula, we get \(a_9 = 1215 * (\frac{1}{3})^{(9-1)} = 0.185\).

Step 7 ：Final Answer: The 9th term of the sequence is \(\boxed{0.185}\)