What Is an Arithmetic Sequence?

What Is an Arithmetic Sequence?

An arithmetic sequence is a sequence of numbers where there is a definitive pattern between the consecutive terms of the series. In general, arithmetic sequences can be represented by x = a + d(n - 1).

A mathematical sequence is a set of values in some order. In order for a sequence to be considered arithmetic, the terms of the sequence must have a common difference from one term to the next. For example, the sequence of counting numbers (1, 2, 3, 4, etc.) is arithmetic. The difference from each term to the next is 1. Each term can therefore be represented by x = a + d(n - 1), where "a" is the first term in the sequence, "d" is the difference between each term, and "n" is the number of the term in the sequence.

There are two types of arithmetic sequences: finite and infinite. A finite sequence has some definite number of terms whereas an infinite sequence continues its pattern and has a value for any "n." Although the pattern is described as the difference between numbers, it can actually be either positive or negative. This difference determines the growth of the arithmetic sequence. If the difference is positive, the terms grow toward infinity. If the difference is negative, the terms decrease toward negative infinity.

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