NOTE: This is a rant expressing my feelings about "the next number" questions.
Where to start?
Puzzling.SE is a site about unique content and possibly derivatives from that content, if they are unique enough.
However, "sequence" questions as I call them are a perfect example of.... not this.
The issue I have is that they are easy to make, and usually don't require a lot of thinking.
You can think of any sequence, make a number for it, and then deny any answers that aren't said number. There are infinite mathematical theorems that could work for one series given, and so there are infinite unique answers that could be given.
This, of course, isn't what Puzzling.SE is for.
This issue is sort of like the whole lateral-thinking problem: people are using that tag to justify nonsensical answers.
Puzzling.SE, like the whole StackExchange family, is a Q and A site: ask a question, get an answer. The problem with these sequence questions, however, is that they could have any answer. This is a completely random sequence I made up in my head: 6, 7, 20, 46, 100
I bet you, if I posted that, not only would I get upvotes, I would be able to only select one answer, even though all the others are valid. This is the problem with lateral-thinking, and the problem with sequence questions.
Simple: don't allow these questions on Puzzling.
And if it's a lack of moderation that causes these to flourish, increase moderation.
My opinion is that sequence questions do not express the creativity of this site, and should not be allowed / should be marked off-topic or too broad.
If you agree or disagree with me, feel free to reply to this question explaining why.