successively; one after another; sequentially
Describes actions or events occurring in order, one by one, without skipping. Often used in formal, technical, or procedural contexts.
We will solve the problems one by one.
The data will be updated sequentially.
Please report the situation on site as things progress.
We plan to fix the problems one by one as we go.
This program processes the data one item at a time.
一斉に means 'all at once, simultaneously', the opposite of 逐次's one-by-one, sequential sense.
Compound of 逐 (chase, pursue, one by one) and 次 (next, order). The meaning 'successively' arises naturally from the kanji components.