Show last node of every term in one Views
Create a view to show content
Add page display and set path setting to news/%
Add contextual filter "Has taxonomy term ID"
Add sort criteria "Authored on (desc)"
In pager settings check "Display a specified number of items" and set "Items per page" setting to 1.


Note that this will produce URLs with numeric term IDs (i.e. news/123).
To make use of term names you need to configure a relationship to the term so you get the information about the term into view, then use term name contextual filter.