The adverb 连续 emphasizes that the same actions are performed sequentially one after another or for a certain period of time.
After 连续, we place a word denoting either an action or the time that an action takes place.
The teacher has been conducting a lesson for two hours straight
lǎoshī liánxù jiǎng le liǎng gè xiǎoshí de kè
It was her third consecutive victory
zhè shì tā liánxù huòdé de dìsān cì shènglì
The city has been attached for four consecutive days