Determine the common ratio $r$, the fifth term, and the $n$th term of the geometric sequence. $7, \frac{14}{3}, \frac{28}{9}, \frac{56}{27}, \ldots$ \[ r= \] \[ a_{5}= \] \[ a_{n}= \]

Step 1 ：The common ratio of a geometric sequence can be found by dividing any term by the previous term. So, to find the common ratio \(r\), we can divide the second term by the first term.

Step 2 ：The \(n\)th term of a geometric sequence can be found using the formula \(a_n = a_1 \cdot r^{(n-1)}\), where \(a_1\) is the first term, \(r\) is the common ratio, and \(n\) is the term number.

Step 3 ：The fifth term can be found by substituting \(n = 5\) into the formula.

Step 4 ：\(a_1 = 7\)

Step 5 ：\(a_2 = 4.666666666666667\)

Step 6 ：\(r = 0.6666666666666667\)

Step 7 ：\(a_5 = 1.3827160493827169\)

Step 8 ：\(a_n = 1.3827160493827169\)

Step 9 ：The common ratio \(r\) is approximately \(0.67\), the fifth term \(a_5\) is approximately \(1.38\), and the \(n\)th term \(a_n\) is also approximately \(1.38\) when \(n = 5\).

Step 10 ：Final Answer: The common ratio \(r\) is \(\boxed{0.67}\), the fifth term \(a_5\) is \(\boxed{1.38}\), and the \(n\)th term \(a_n\) is \(\boxed{1.38}\) when \(n = 5\).