Hint: The sequence involves both adding and multiplying in some way.
The sequence is created using: +1 x1 +2 x2 +3 x3 +4 x4 +5.
Can you find three words...
...which contain two consecutive i's.
Hint: The words begin with the letters R, S, T.
Answer: RADII, SKIING, TAXIING.
You could also have GENII.