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Two things are consecutive if one follows the other directly. When our concern is the natural numbers, consecutive numbers are next to each other in the number line. The sequence:

1, 2, 3, 4, 5, ... , n is the list of the first n consecutive numbers.

If there is any 'gap' in the sequence it is non-consecutive:

2, 3, 4, 5 is a list of 4 consecutive numbers, whilst 3, 5, 7, 9 isn't (even though they are still in order). :)

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