If your account is compromised, one of the first things you should do is…

Changing your password immediately is the most critical first step when your account is compromised. This prevents the unauthorized user from continuing to access your account and making further changes or posts. While contacting Twitter Support is important, it should happen after you've secured your account. Closing your account is a drastic measure and should only be considered after attempting to regain control. Tweeting about the compromise might alert your followers, but it doesn't secure your account and could even be used by the attacker.