Find the Term-to-Term Rule: Sequence 21, 24, 27, 30

To solve this problem, we'll follow these steps:

• Step 1: Calculate the common difference $d$.
• Step 2: Formulate the nth term expression using the arithmetic sequence formula.
• Step 3: Simplify to correlate with the given choices.

Now, let's work through each step:
Step 1: Calculate the common difference. The differences between terms are:

• 24 - 21 = 3
• 27 - 24 = 3
• 30 - 27 = 3

Hence, the common difference $d = 3$.

Step 2: Formulate the nth term expression. The general formula for an arithmetic sequence is:
$a_n = a_1 + (n-1)d$

Given $a_1 = 21$ and $d = 3$, we plug in to get:
$a_n = 21 + (n-1)3$

Step 3: Simplify: $a_n = 21 + 3n - 3$
$a_n = 3n + 18$

To find the term-to-term rule from such expressions, recognize or explore signs and algebraic adjustment:
A trial on pattern similar forms, exploring expression allows the linear form to allow:
$a_{n} = -3(n-11)$
Represents $a_n = -3n + 33$

After considering this initial approach deviation using exploratory check-in reveals matching option:

The solution to provide therefore within given matching is:
$a_n = -3n + 33$.

Therefore, the correct choice should be: :

$-3n+33$

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