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Recursive and Explicit Pattern RulesA recursive pattern rule is a pattern rule that tells you the beginning number of a pattern and how the pattern continues. For example, a recursive rule for the pattern 5, 8, 11, 14, … is start with 5 and add 3 each time.A common difference is the difference between any two consecutive terms in a pattern. Not all patterns have a common difference. For example:the pattern 5, 10, 15, 20, … has a common difference of 5.The pattern 1, 4, 9, 16, … has no common difference.An explicit pattern rule is a pattern rule that tells you how to find the term value for any term in the pattern without listing all the terms before it. This equation can be used only if the pattern has a common difference.For example, An explicit pattern rule uses the first term and the common difference to calculate the value of any term in the pattern. Explicit pattern rule equation:___ term = first term value + [( ___term number -1) x (common difference)]For the pattern 5, 8, 11, 14, … first term is 5 and the common difference is 3.To calculate the 20th term, use this explicit pattern rule equation:20th term = first term value + [( term number -1) x (common difference)]20th term = 5 + (19 x 3)20th term = 5 + 5720th term = 62 ................
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