A puzzle in which the hidden pattern behind a given sequence of numbers (and, often, the next term) is to be found. Use with [sequence]
A 'number sequence' is a series or collection of numbers presented in a particular order according to a specific logical rule. In number-sequence puzzles, the aim for the solver is usually to deduce or discover the rule behind this ordering, and/or supply the next - or missing - number(s) in the sequence.
The hidden pattern is often mathematical in nature (in which case, the mathematics tag may also be used), but sometimes is derived from common knowledge, structures (e.g. Morse code), or language (e.g. alphabetical ordering).
For some advice on how to create interesting number sequence puzzles (and also what not to do), see this meta question.
Please note: Many common "brainteaser" number sequences, such as the "Look and Say" sequence, have already been posted on Puzzling Stack Exchange. Before sharing an interesting sequence that you have found published or presented elsewhere, please make sure to search for duplicates using at least the first few terms of the sequence, and avoid re-posting questions found to have been posted previously.
