Successive is a word for things (or people) that follow each other in time. If three presidents in a row were over sixty, you could say, "Three successive presidents were over sixty."
Successive is a word that comes up often when you're looking at the history of something. Back in the 1960s, eight successive Boston Celtics teams won the NBA championship. In school, if you do very well, you could get an A in three successive math classes. Even though successive has the word success in it, it's not necessarily a good thing: you could also miss ten successive free throws.