What is the next term of the arithmetic sequence?

To find the next term in the arithmetic sequence \(3, 9, 15,\), we first need to determine the common difference.

We subtract the first term from the second term:
\[
9 - 3 = 6
\]
Then, we subtract the second term from the third term:
\[
15 - 9 = 6
\]

The common difference \(d\) is \(6\).

Now, we can find the next term by adding the common difference to the last term in the sequence:
\[
15 + 6 = 21
\]

Thus, the next term of the arithmetic sequence is \(\boxed{21}\).