This sequence follows the pattern of triangular numbers: 0, 1, 3, 6, 10, 15, 21... Each term increases by 1, then 2, then 3, then 4, then 5, then 6. The difference between consecutive terms increases by 1 each time: 1-0=1, 3-1=2, 6-3=3, 10-6=4, 15-10=5, so 21-15=6.