Yeah it’s a bit confusing. It’s also confusing when you see them written because they’re actually written usually with a nested subscript. Like
a
n
k
With the k smaller than the n which is in turn smaller than the a. Sequences of all kinds are just a function from the integers to the reals so I don’t know why we had to go and invent a whole new notation for them just to be extra obtuse.
a(n_1), a(n_2), a(n_3), ... is a subsequence of a_n and is denoted a(n_k).
So the indexes don't need to be contiguous, just increasing.
So in your example 2, 1, 1/2, 1/3, ... is a decreasing subsequence.
edit: changed to using function-style notation because the nested subscript notation looks confusing in ascii