The only rule for any set is that given any element [number], you should be able to determine whether or not it is a member of the set.
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A sequence is a set of numbers, which are identified by their position in the set. That is to say, there is a function mapping the counting numbers {1, 2, 3, ... } to the set. The counting numbers may include 0. There may or may not be a rule governing the numbers. For example, a random sequence, by definition, should have no rule.
Anything you like. You specify whatever rule you like and the resulting set of numbers is the sequence based on that rule.
CALOCUS
It is an ordered set of elements. These elements may or may not be numbers, there may or may not be a defining rule - for example a sequence of random numbers.
There are infinitely many cubic functions that can be the rule for the above set of numbers. The simplest, though, is the linear rule: Un = 8n - 1 for n = 1, 2, 3, ...