3, 12, 21, 39, 75, 138, 237
Let's look at the differences between each number:
9, 9, 18, 36, 63, 99
Those are all divisible by 9, so let's try:
9(1), 9(1), 9(2), 9(4), 9(7), 9(11)
There's a pattern:
1, 1, 2, 4, 7, 11
The differences between those:
0, 1, 2, 3, 4
The pattern 0, 1, 2, 3, 4 should continue like this: 0, 1, 2, 3, 4, 5, 6, 7 and so on.
The pattern 1, 1, 2, 4, 7, 11 should continue like this: 1, 1, 2, 4, 7, 11, 16, 22, 29 and so on.
The pattern 9(1), 9(1), 9(2), 9(4), 9(7), 9(11) should continue like this: 9(1), 9(1), 9(2), 9(4), 9(7), 9(11), 9(16), 9(29) and so on.
The pattern 9, 9, 18, 36, 63, 99 should continue like this: 9, 9, 18, 36, 63, 99, 144, 261, and so on.
The pattern 3, 12, 21, 39, 75, 138, 237 should continue like this: 3, 12, 21, 39, 75, 138, 237, 381, 642, and so on.