Here's how it breaks down:
* In-: A prefix meaning "not" or "the opposite of"
* Con-: A prefix meaning "with" or "together"
* Sequi: The Latin root meaning "to follow"
* -ential: A suffix meaning "relating to" or "characterized by"
Therefore, "inconsequential" literally means "not following together" or "not following with." This implies something that is not connected or important, hence its meaning of "unimportant" or "of no consequence."