What is the nth term rule for the pattern: 3, 6, 9, 12, 15,...?

$6 - 3 = 3$
$9 - 6 = 3$
$12 - 9 = 3$
$15 - 12 = 3$
Since the difference between consecutive terms is constant, this is an arithmetic sequence with a common difference ($d$) of 3.

The first term ($a_1$) is 3.

The formula is $a_n = a_1 + (n-1)d$.

For $n=1$, $a_1 = 3(1) = 3$
For $n=2$, $a_2 = 3(2) = 6$
For $n=3$, $a_3 = 3(3) = 9$
The rule $a_n = 3n$ correctly generates the terms of the pattern.

Comparing this with the given options:
A. $a_n = n+2$
B. $a_n = 3n$
C. $a_n = 3n+1$
D. $a_n = n+3$

The correct option is B.

The final answer is $\boxed{\text{B. } a_n = 3n}$.