What is the difference between 连续， 陆续， 接连， and 一连？
As all four words have very similar meanings, here's an attempt to explain the slight differences: 

连续 emphasize on the consecutive-ness - there're no breaks in between.
陆续 emphasize on counting - in a sense of 'keep it coming'.
接连 emphasize on succession / connection.  'one after the other' fits here.      
一连 is the same as 连续 but in a sense of shorter range in terms of usage.