Find the Variable Expression n for Sequence 12, 18, 24, 30, 36

To solve this problem, we first recognize that the sequence $12, 18, 24, 30, 36$ is an arithmetic sequence.

• Step 1: Identify the first term $a_1$.

  The first term $a_1$ of the sequence is $12$.

• Step 2: Determine the common difference $d$.

  The difference between consecutive terms is consistent: $18 - 12 = 6$. Hence, the common difference $d = 6$.

• Step 3: Formulate the expression for the general term.

  The general term of an arithmetic sequence is given by $a(n) = a_1 + (n-1) \times d$.

• Step 4: Substitute the identified values into the formula.

  Substituting the known values, we get $a(n) = 12 + (n-1) \times 6$.

Thus, the expression for the general term of the given sequence is $a(n) = 12 + (n-1) \times 6$, which corresponds to choice 3.