Highlight one or more cells in the sequence and drag the bottom right-hand corner to the cells you want to fill with that sequence. If, for example, you highlight the first three rows that are filled with 1, 2 and 3 and drag down the bottom-right corner, it'll determine the pattern and fill accordingly. If you only highlight one cell, it may copy that number to all of the target cells or it may fill them in sequentially -- the more data you give it (highlighted cells before you grab and drag), the better it'll guess what the pattern is. If it chooses incorrectly (usually based upon what you did last time -- either copy cell contents or continue the sequence), there's a little icon that pops up after the operation on the lower-right corner. Select that icon and select "Fill Series."
This works with Excel, but not sure about tables in Word.