Find the missing numbers in the following sequence: 3, 6, 24, 30, 63, 72, ?, ?, 195, 210
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Find the missing numbers in the following sequence: 3, 6, 24, 30, 63, 72, ?, ?, 195, 210
117, 123
120, 132
123, 135
135, 144
The series follows an alternating pattern of adding consecutive squares and consecutive natural numbers. Starting with 3, we add 3 (which is the difference of 6 minus 3) to get 6, add 18 to get 24, add 6 to get 30, add 33 to get 63, and add 9 to get 72. The additions are 3, 18, 6, 33, 9, where the sequence of additions alternates between an increasing multiple of 3 and an increasing multiple of 3. Adding 48 (which is 3 times 16) to 72 gives 120, and adding 12 to 120 gives 132.