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What is the definition of a sequence?

(A) An ordered arrangement of a set of numbers
(B) A list of numbers in ascending or descending order
(C) A mathematical expression that shows the relationship between two or more variables
(D) A pattern of numbers that follows a specific rule

User Hmartos
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Final answer:

A sequence is an ordered arrangement of a set of numbers, which aligns with definition (A). It often follows a specific rule or pattern, but not all sequences are in ascending or descending order, and they are not necessarily expressions of relationships between variables.

Step-by-step explanation:

The definition of a sequence can vary slightly in context but generally, a sequence is (A) An ordered arrangement of a set of numbers. In mathematics, a sequence is a list of numbers (elements) arranged in some particular order. It is not necessarily in ascending or descending order, which eliminates option (B). Unlike a mathematical expression or function, which describes a relationship between two or more variables, a sequence itself may not explicitly define relationships between its terms like in option (C). Option (D), 'A pattern of numbers that follows a specific rule', is quite close to defining a sequence but could be seen as a subcategory of sequences, as not all sequences follow a discernable pattern, though many do and are studied because of these.

Consider the sequence 3, 6, 9, 12, ... where each term after the first is obtained by adding 3 to the previous term. This sequence is an ordered set of numbers following a specific rule (addition of 3), and it happens to be an arithmetic sequence—a type of sequence with a constant difference between consecutive terms.

User Orbiteleven
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