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Q: How do you find the rule of a sequence of numbers?

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Anything you like. You specify whatever rule you like and the resulting set of numbers is the sequence based on that rule.

It is a sequence of numbers. That is all. The sequence could be arithmetic, geometric, harmonic, exponential or be defined by a rule that does not fit into any of these categories. It could even be random.

1, 4, 7, 10, 13, …

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.

The rule for the sequence is an = xn-1 + xn-2The sequence of numbers, 1, 1, 2, 3, 5, 8, 13, . . . , in which each successive number is equal to the sum of the two preceding numbers.

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It is a sequence of numbers. That is all. The sequence could be arithmetic, geometric, harmonic, exponential or be defined by a rule that does not fit into any of these categories. It could even be random.

Anything you like. You specify whatever rule you like and the resulting set of numbers is the sequence based on that rule.

A sequence is an ordered set of numbers. There may be a rule governing the sequence such that, if you know the numbers in the sequence up to a particular point, the rule will allow you to deduce the value of the next number in the sequence. That rule - if it exists - is the sequential pattern.

1, 4, 7, 10, 13, …

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.

An arithmetic sequence is a list of numbers which follow a rule. A series is the sum of a sequence of numbers.

The rule for the sequence is an = xn-1 + xn-2The sequence of numbers, 1, 1, 2, 3, 5, 8, 13, . . . , in which each successive number is equal to the sum of the two preceding numbers.

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.

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.

It appears that a number of -79 is missing in the sequence and so if you meant -58 -65 -72 -79 -86 then the nth term is -7n-51 which makes 6th term in the sequence -93

Those are the first four prime numbers.

The rule method is used to describe any set of numbers, so put any sequence of numbers in brackets and there you go.