Find any of the values $a_{1}, r, a_{n}, n$, or $S_{n}$ that are missing from the geometric sequence.
\[
r=\frac{5}{3}, n=5, S_{5}=\frac{1441}{3}
\]
The value of $a_{1}$ is 27 .
(Simplify your answer. Type an integer or a fraction.)
The value of $a_{5}$ is
(Simplify your answer. Type an integer or a fraction.)
Answer
Final Answer: The value of \(a_{5}\) is \(\boxed{\frac{625}{3}}\).
Step 1 ：We are given the common ratio \(r\), the number of terms \(n\), the sum of the first \(n\) terms \(S_{n}\), and the first term \(a_{1}\). We are asked to find the fifth term \(a_{5}\).
Step 2 ：The formula for the nth term of a geometric sequence is \(a_{n} = a_{1} * r^{(n-1)}\). We can use this formula to find \(a_{5}\).
Step 3 ：Substitute the given values into the formula: \(a_{1} = 27\), \(r = \frac{5}{3}\), and \(n = 5\).
Step 4 ：Calculate \(a_{5} = 27 * (\frac{5}{3})^{(5-1)} = \frac{625}{3}\).
Step 5 ：Final Answer: The value of \(a_{5}\) is \(\boxed{\frac{625}{3}}\).
