From John-Paul Green’s Flashy Maths try ‘Sequences‘ to generate linear sequences and predict the nth term.
To identify an integer sequence try the Online Encyclopedia of Integer Sequences.
Simply type in your sequence and choose Search.

Note that you can list, graph or even listen to the sequence!
There are further links at the foot of the page, try Puzzles for some unusual sequences. Some of these are fun to try with students, try the eban sequence: 2, 4, 6, 30, 32, 34, 36, 40, 42, 44, 46, ….
Alternatively simply type the sequence into Wolfram Alpha.

Typing ‘Sequences’ into WolframAlpha shows several possibilities for queries on sequences.
For more on WolframAlpha see the WolframAlpha pages.