Hi.
The best I have come up with for no. 1 (and it's not good) is the answer
7.
Spell out the given numbers ('two hundred and seventy-three', 'seventeen', 'eleven' & 'five') and the number of letter 'e' in each is 5, 4, 3 & 1. 'seven' with its two 'e's could fit the pattern between 11 & 5.
JimC