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.