Find a formula for the general term $a_{n}$ of the sequence assuming the pattern of the first few terms continues. \[ \{6,3,0,-3,-6, \ldots\} \] Assume the first term is $a_{1}$

Step 1 ：Assume the first term is $a_{1}$

Step 2 ：The sequence appears to be decreasing by 3 each time. This suggests that the sequence could be an arithmetic sequence, where each term is found by adding a constant difference to the previous term. In this case, the difference appears to be -3.

Step 3 ：The general formula for an arithmetic sequence is $a_{n} = a_{1} + (n-1)d$, where $a_{1}$ is the first term, $n$ is the term number, and $d$ is the common difference.

Step 4 ：In this case, $a_{1} = 6$ and $d = -3$.

Step 5 ：Let's substitute these values into the formula and simplify to find a formula for $a_{n}$.

Step 6 ：The simplified formula for the nth term of the sequence is $a_{n} = 9 - 3n$. This formula should generate the terms of the sequence when we substitute $n = 1, 2, 3, \ldots$

Step 7 ：Final Answer: The formula for the general term $a_{n}$ of the sequence is \(\boxed{a_{n} = 9 - 3n}\).