Why doesn't "Прошлой неделе." work?
Seconded. It was duolingo's suggestion for the translation.
Duolingo actually recommended на прошлой неделе, but I still can't tell why it's different
In context, that is correct. I think because it is nominative, out of context, the correct declination is "-я".
This may be used in response to a question.
Q: "Когда ты работал?"
A: "Прошлая неделя."
Q: When did you work?
A: Last week
почему «последная» не работает?
"Последняя неделя" means that this week is the last, there won't be any other week after it. Like "the last week of the vacation".
"Прошлая неделя" is the previous week, actually. The week that came before the current one.
I'm not sure this word can be used in the meaning of "previous", but even if can, it is spelled последняя.
what is the difference between прошлая and прошлый?
Прошлая is feminime and прошлый is masculine
Is the difference between «прошлая неделя» and «неделю назад» that the latter could go back more than one, and the former refers only to the very recent one, while both could translate “last week” in the forms given above?
What's the difference with "на" in the beginning ?
Ha is used in context.
"На прошлой неделе, я бежал"
Last week, I ran
"Я работал на прошлой неделе"
I worked last week
In this case, you can translate "на" as "during". I worked DURING last week.