If someone is being obsequious, they are trying so hard to please someone that they lack sincerity in their actions towards that person.
If you sequester someone, you keep them separate from other people.
If a song, idea, or activity segues into another song, idea, or activity, it changes smoothly into it or is followed immediately by it without any stops or breaks.
Inconsequential matters are unimportant or are of little to no significance.
Something that is subsequent to something else is later than or after it in time.
The sequence of something, such as an event or action, is the order in which it takes place.
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