Consecutive, successive, sequent, sequential, serial are comparable when meaning following one after the other in order.
Consecutive and successive apply to objects which follow one another without interruption or break.
But consecutive is somewhat more emphatic, stressing the immediacy of the succession, the regularity or fixedness of the order, and the close connection (as in time, space, or logic) of the units while successive is applicable to things that follow regardless of differences (as in duration, extent, or size) or of the length of the interval between the units; thus, one would speak of nine, ten, and eleven as consecutive numbers since they follow one another in immediate and regular order, but of flashing the successive numbers three, eleven, and nine on a screen since the order would then be neither immediate nor regular; one would speak of successive (not consecutive) leap years since the order though regular is not immediate and of successive strokes of a piston since, though immediate, it need not be regular.
Consecutive is also applicable to a person or to thought that manifests logical sequence.
Sequent and sequential apply to an arrangement or to things (sometimes a thing) following a sequence (as a causal, logical, or chronological sequence) or some settled order.
Serial implies that the thing or things so qualified form a series or will appear as a series; it therefore suggests likeness or uniformity in the units and, usually, a prearranged order especially in time or space.