I have a question to ask. If there is a change in formula field , will it fire apex trigger after update?
Please let me know if that happens then only I can do the development likewise.
No, a formula field changing doesn't change the updated by, and doesn't count as a record update. Behind the scenes formula fields aren't stored as part of the record in the database, instead they use logic embedded in SQL at query time, so the values don't persist, instead they're generated on the fly when the object is queried.