Number of sub-sequences in a given sequence

Question

If I am given a sequence X = {x1,x2,....xm}, then I will have (2^m) subsequences. Can anyone please explain how can I arrive at this formula intuitivel

Answer 1

If you have a sequence S, what happens when you add a new element x to the end of S?

All the subsequences of S are still subsequences of your new sequence. So are all those subsequences with x added at the end.

Voilà! Every time you add an element, you double the number of subsequences.