Answer:
87
Step-by-step explanation:
Such "find a pattern" problems can always be answered a number of ways.
Here, the alternating pattern (6, 12, 6, 12, ...) of first differences doesn't seem to hold. However, the first differences of alternate terms does seem to be constant: 33, 51, 69 all have a common difference of 18.
The next term in that sequence is 69+18 = 87.
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The other terms seem to have increasing differences:
57 -39 = 18
84 -57 = 27
If that pattern continues, then the second missing term will be 84 +36 = 120.
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So, one way to extend the sequence is ...
33, 39, 51, 57, 69, 84, 87, 120, 105, 165, ...
The rule is that the sequence alternates a linear sequence and a quadratic one.
