In the last 30 days you've played 8 rapid games and gone from 272 to 359 ELO.
Going from 272 to 359 in 30 days isn't particularly "fast" IMHO but doing it over only 8 games is pretty quick. So it depends on what you mean by "improving fast" in the first place
Yeah start with rapid. I did that too. Just saw your profile, I think you will improve quickly.
I do everything I can to improve but still am below 400 rapid, and below 300 in blitz and bullet. *blushes°
you will be much better than me in just few days it seems. 
I believe everyone (except me) can improve quickly and get to 700-1000 rapid at some point.
edit: now even only 187 in blitz =-O wow am I weak. xD I give my best in every game and still I get sexy losses!
Getting choached by a strong, experienced coach is not required, but it speeds up the process of improving dramatically and is the fastest way to improve.