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.
**List** has a very precise meaning in mathematical or computer science domains, which seems to apply here. 

Would a *”a **list** of tasks”* make sense?

> 
> In computer science, a **list** or **sequence** is an abstract data type that represents a countable number of **ordered** values, where the same value may occur more than once. 
>  <https://en.wikipedia.org/wiki/List_(abstract_data_type)>
> 
> 
> 

This is in contrast with a **set** which has no order.