The next three numbers in the sequence are fifty-two, sixty-seven and eighty-four. The pattern consists of adding the next odd number in sequence to the last number. Starting with the seven, five is added to make twelve. After five, the next odd number is seven. When added to the last number, twelve, the result is nineteen. The next odd number is nine, added to nineteen, equals the number twenty-eight. Finally, the next odd number is eleven, added to twenty-eight, equals thirty-nine.
Therefore, the next three numbers must follow the same pattern. Thirteen added to thirty-nine equals fifty-two. Fifteen, the next sequential odd number, added to fifty-two equals sixty-seven. And finally, the next odd number in sequence is seventeen, when added to sixty-seven equals eighty-four.