Here are a few examples:
* The company was experiencing financial difficulties, and consequently, they had to lay off some employees.
* The storm caused widespread power outages, consequently leaving many people without electricity.
* She studied hard for the exam, and consequently, she achieved a high score.
As you can see, "consequently" is often used to introduce a result or consequence of something mentioned earlier in the sentence. It usually follows a comma, but you can also use a semicolon if the clauses are long or complex.