Arithmetic Sequence

Arithmetic Sequence

Sequence of numbers in which the difference r between two consecutive terms is constant.

Synonym for arithmetic progression.

The constant difference between two consecutive terms is called the difference of the arithmetic sequence.


Consider the number sequence S = {1, 3, 5, 7, 9, 11, …}
Notice that there is a constant difference of 2 between two consecutive terms. This means that it is an arithmetic sequence defined by: S = {x ∈ \(\mathbb {N}\) | x = 2r + 1}.

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