Anything you like. You specify whatever rule you like and the resulting set of numbers is the sequence based on that rule.
Chat with our AI personalities
The phrase "first difference" is usually associated with a sequence of numbers: a(1), a(2), a(3), a(4), ... . The sequence may have a simple rule for generating the numbers , a complicated rule or, if it is a random sequence, no rule at all.The sequence of first differences is a(2)-a(1), a(3)-a(2), a(4)-a(3), ...
A number sequence is an ordered set of numbers. There can be a rule such that the next number in the sequence can be determined by the values of some or all of the preceding terms in the sequence. However, the sequence for a random walk illustrates that such a rule is not necessary to define a sequence.
A single number, such as 12631.5, does not make a sequence.
Without further terms in the sequence, it is impossible to determine what the rule in the sequence is.
Since a given sequence of numbers can be designed to follow any rule, you have to use a system of trial and error to see if you can discover the rule. Sometimes the rule is obvious, sometimes it is extremely complicated. Try to invent a rule which would produce the sequence that you observe.