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No, the Fibonacci sequence never ends. It just keeps on going!
There is the Morris number sequence and the Fibonacci number sequence. The Padovan sequence. The Juggler sequence.
I just know the Fibonacci sequence:
0,1,1,2,3,5,8,13,21,34,55,89,144,233,377
Morris number sequence: 1 11 21 1211 111221 312211...
cuz it just IS.
airline reservation system sequence diagram
From what I know, it is just called "next term in sequence"
For a unknown term, just call it the "nth term".