Things in a sequence come one after another, as in a number sequence of 1, 2, 3, 4. A consequence comes after, or as a result of something you do, for example, "He was given a traffic ticket as a consequence of running the red light."
A consequence is a "result" or "conclusion," and the Latin sequī, "to follow," is part of its history. Most actions and acts of nature have a consequence that follows as a result. When people do something wrong, like rob a bank, the consequence will probably be prison time. If an organization works for good and finds a cure for cancer, on the other hand, people will get better as a consequence. When something occurs in nature, like a tornado touching down, destruction might be the consequence.