Question: I'm looking for a word that describes the backward, dependency between items that must be completed in a specific order, one after another.

"A series of *interdependent* tasks."

Is there a word that is more specific than interdependent? I don't want to imply that multiple tasks might depend on multiple other tasks. I also don't want to imply that two or more tasks might share dependencies between themselves at the same time. Only one task at a time has dependency on its prerequisite and the dependency relationship only goes in one direction.

Answer: 
You can use **subsequent**

As in, set of subsequent tasks.
[Procedure](https://en.oxforddictionaries.com/definition/procedure) : A *series* of actions conducted *in a certain order* or manner.