An arithmetic sequence (sometimes called a “progression”) is a particular type of sequence that has an initial value, as with all sequences. A proper arithmetic sequence has a common difference, that when added to the initial number and each consecutive number, provides the arithmetic sequence. Keep in mind that this common difference can be a positive or a negative value so the arithmetic sequence might be increasing or decreasing regularly. In addition, an arithmetic sequence may begin with a negative number as long as the sequence progresses by the constant value from that starting point.
An arithmetic sequence example would look like this:
1, 5, 9, 13, 17, 21, 25, 29, … with a common difference of 4.
Look for the common difference by subtracting the preceding value from the current value and ensuring this holds for the following numbers.
Is this sequence an arithmetic sequence? 2, 1, 3, 4, 7, 11, ….
If we have 1, 4, 7, 10, 13, 16, 19, 22, 25, …, what is the number following “25?”
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