Showing Latest Featured Image in Current Category

I have a custom magazine type template I am trying to code.

I am trying to use the most recent featured image for the most recent post in a category as a header image in that specific category.

Example:

Show most recent post’s featured image for category 1 on category 1’s page. (So each category has a featured image on its page and it will always be the most recent posts featured image).

Does this make sense?