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

Each element is either in a subsequence or not. Therefore, starting with the first x1 there are two sets of subsets: those with x1 included and those without. Same can be done with the smaller sub-problem {x2,...,xm}. Therefore you finally yield 2^m.