Consecutive sets are those where three or four of your sets have numbers that ascend in some pattern. These patterns must all be in the same suit. Since these patterns always have either a middle sequence or triplet, they do not combine with any of the terminals and honors patterns.
7.0 Consecutive Sets
7.1 Nine-Tile Straight : 40
7.2.1 Three Consecutive Triplets : 100
7.2.2 Four Consecutive Triplets : 200
7.1 Nine-Tile Straight
This pattern is recognized in MCR and riichi. One sequence of 123, one of 456, and one of 789, all in the same suit. It is fairly easy to defend against, but since it is not a huge hand, people may risk completing their own first. Frequently combines with four sequences, half- or full-flush.
7.2.1 Three Consecutive Triplets
7.2.2 Four Consecutive Triplets
Three or four triplets (pungs) of consecutive numbers in the same suit. Having one or two of these sets concealed is a huge boon, because your opponents will try very hard to stop you from completing these patterns. Or rather, they will try very hard not to be the person who throws your winning tile. If you are lucky, your sets are middle numbers, so both ends are open, or at least your opponents think they are.
Both patterns often combine with all simples or some kind of flush.
Three Consecutive Triplets often combines with four triplets, or a value set.
Four Consecutive Triplets is not a limit hand, so it always combines with Four Triplets. If you manage to add one suit, you have a near-limit 310 points. This is a great big hand that is not so hard to get as to be ridiculous.