No, you should not necessarily downvote questions that you don't find personally useful - if that were the case, then $99\%$ of questions should be downvoted by $99\%$ of users, which would make the entire process silly.
In general, there are a few reasons that I personally will downvote (but I don't downvote all posts of these types):
(1) The question is extremely poorly phrased, and missing crucial details.
(2) The question is clearly lacking any research effort, or is a mere problem statement that came from the OP's homework.
(3) The question involves spam or is offensive in some way.
(4) The question is very clearly off-topic here.
In general, I will almost never downvote questions that are tagged with things such as reference-request, notation, terminology and so on, unless they are egregiously in violation of the first two points above. It can be very difficult to research what a concept is called if you don't have a name for it, so I think we should be particularly forgiving for these sorts of questions. (And no, I don't agree with downvoting the question you mention in your post). There also seems to be a consensus that questions with tags like contest-math should be given more leeway than other posts, too.
Your mileage may vary - the question of whether my point (2) is valid is a debate that has consumed meta for years. Regardless, I only downvote a question when I think it's a bad question; so "not being good" isn't usually sufficient for me to downvote.
Regarding your comments about whether you should downvote things that "seem to be not useful to SE goals," note that the purpose of SE is to compile a list of questions with authoritative answers - especially considering that homework questions are frequently assigned (or at least seen) by a general audience, I don't see how homework questions are any less useful with respect to SE as a concept.
Finally, regarding the question that you posted that was downvoted: It's stated without any thoughts or efforts (see point (2)), and there's not really a definitive mathematical answer to any of these "find the next term in the sequence" questions.