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Arithmetic Sequences

Arithmetic Sequences

Arithmetic Sequences

A list of numbers, referred to as terms, in which the numbers are ordered is known as a sequence. In this chapter arithmetic sequences are introduced and their specific characteristics are studied.
When subtracting two consecutive terms of an arithmetic sequence the difference is always the same. It does not matter which two consecutive terms that were used to calculate this difference. This difference is known as the common difference of the arithmetic sequence. By showing that there exists a common difference for a sequence is enough to prove that the sequence is arithmetic.
Arithmetic sequences can be compared to linear functions, since when graphed the terms of an arithmetic sequence can be shown to fall on a line. When making this comparison the common difference corresponds to the slope of the line. If the terms of an arithmetic sequence are graphed they are displayed as collinear points. However, an arithmetic sequence and a linear function are different in that a sequence is discrete whereas a linear function is continuous.
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