次第に + [verb/adjective of change]
Standalone adverb; placed before the predicate describing gradual change. Often pairs with なる、変わる、増える、減る、〜てくる、〜ていく.
次第に (しだいに次第に) is an adverb meaning "gradually" or "little by little". It describes a change that happens progressively over time, not suddenly. It is used to express that something shifts or transforms in a slow, continuous manner.
次第に is placed before the verb or adjective that describes the change. It often pairs with verbs of change such as なる (to become), かわる変わる (to change), ふえる増える (to increase), and へる減る (to decrease), as well as with ~てくる and ~ていく to emphasize the ongoing nature of the change.
Both 次第に and だんだん mean "gradually," but 次第に is more formal and literary. だんだん is common in everyday conversation, while 次第に is more often found in written language, news, narration, and formal speech.
Compare with the more casual equivalent:
Both sentences have the same meaning, but the first sounds more formal.