It's better if you add a 地 after 一个接一个. 地 is a special character used after a descriptive phrase to decorate a verb or verb phrase. In English Chinese dictionary we use it to translate adverb too, as in "nicely 漂亮地", "generously 慷慨地", "loudly 大声地". The same is for 的, which is used after a descriptive word or phrase to make it an adjective. For example: "nice 漂亮的", "generous 慷慨的", "loud 大声的".

孩子们一个接一个走进教室 the children one by one into the classroom

我一个一个的吃掉美味的食物。I eat the delicious food one by one.:-P

Thank you Holy Cow, lol. Yes I was unsure about if I should use de. A few people are saying I have to use de, but I saw lots of examples not using it, so I chose to leave it out in places.

better use 一个接一个”地“， sounds more complete to me， but without 地 is ok ，too