An arithmetic sequence is given below.
\[
15,12,9,6, \ldots
\]
Write an explicit formula for the $n^{\text {th }}$ term $a_{n}$.

Step 1 ：An arithmetic sequence is given as \(15,12,9,6, \ldots\)

Step 2 ：The difference between consecutive terms is constant. In this case, the common difference is \(-3\) (since \(12 - 15 = -3\), \(9 - 12 = -3\), and so on).

Step 3 ：The general formula for the \(n^{\text {th }}\) term of an arithmetic sequence is \(a_n = a_1 + (n - 1) \cdot d\), where \(a_1\) is the first term and \(d\) is the common difference.

Step 4 ：In this case, \(a_1 = 15\) and \(d = -3\). So, we can substitute these values into the formula to get the explicit formula for the \(n^{\text {th }}\) term.

Step 5 ：The explicit formula for the \(n^{\text {th }}\) term \(a_{n}\) of the given arithmetic sequence is \(a_n = 15 + (n - 1) \cdot -3\).

Step 6 ：Simplifying this, we get \(a_n = 18 - 3n\).

Step 7 ：\(\boxed{a_n = 18 - 3n}\) is the final answer.