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What does the term first difference mean in math?
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), ...
What make a number sequence?
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.
What is the rule for this sequence 12631.5?
A single number, such as 12631.5, does not make a sequence.
What is the rule for this pattern 2 6 8 14?
Without further terms in the sequence, it is impossible to determine what the rule in the sequence is.
How do you find the rule of a sequence of numbers?
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.
