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 \(\boxed{21}\).