Other than simple inspection, the most basic methods for finding the functions underlying number patterns are common differences and common ratios. To find the common difference or the common ratio, subtract one term from the next, or divide one term into the next, respectively, and repeat for the next term.
Continue ReadingIf the first term in a series or pattern is x less than the second, and the second is x less then the third; this continues, and the common difference is x. A common ratio is the number multiplied by one term that yields the next. For example, 3 is the common difference for the series "1, 4, 7, 10, 13, ..." and is the common ratio for the series "2, 6, 18, 54, ..." These methods can be extended or combined to find higher level patterns.
To find a second difference, create a new sequence from the differences between successive terms in a series. For the series "1, 2, 4, 7, 11, ..." the first differences form the series "1, 2, 3, 4, 5, ..." A common difference of 1 underlies this series and can be used to predict the next terms in the original pattern.
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