y=30x+35
+30, +60, +90, +120, +180
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explain how to find the rule in a numerical pattern
The rule for the pattern is y=x+2. That rule is in the table format in which it would originally be in, but the worded rule would be 'It increases by 2 each time'.
multiply by three
Times one, doubled, times one, doubled...
There are actually more than a pattern rule for that type of sequence. The pattern rule is not obvious. The sequence is actually this: an = 5a(n - 2) for n > 2, such that the seed values are a1 = 1 and a2 = 5. Another pattern rule is the number of palindromes using a maximum of five different symbols. The third one is the Inverse Binomial Mean transformation of the Fibonacci sequence.