Each subsequent number in this sequence is 2 less than the previous. It is extremely likely that the next number in this sequence is 2.
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1, 4, 7, 10, 13, …
A pattern rule is a mathematical expression that describes the relationship between the input and output values in a sequence or pattern. In the context of the number -4, it could represent a pattern rule where each successive number is decreased by 4. For example, if the pattern rule is -4, the sequence could be 10, 6, 2, -2, and so on, where each number is 4 less than the previous one.
12
For a linear sequence (same differences) look for the difference first. E.g.7, 11, 15, 19 ...This has a difference of 4 so the first part of the rule is 4n. (the rule follows the 4 times table)Now compare the sequence to the 4 times table7, 11, 15, 19 ...4, 8, 12, 16 ...Out sequence is always 3 larger than the four times table so we adjust our rule by adding 3. So our final rule is 4n + 3.
The rule for this sequence appears to be adding consecutive prime numbers. The sequence starts with 3, then adds the next prime number 2 to get 4. It then adds 3 (the next prime number) to 4 to get 7, then 5 to 7 to get 12, and so on. Each number in the sequence is the sum of the previous number and the next prime number in order.