Directions: Identify the missing number in the given series. 6, 12, 30, 56, 132, 182, ?

The given series follows an alternating pattern of multiplication and addition. The calculations are 6 times 2 is 12, then adding 18 gives 30, then 30 times 2 is 60, then adding 60 gives 132, then 132 times 2 is 264, then subtracting 82 gives 182. This pattern is inconsistent, but looking at the differences between terms reveals a pattern. The differences are 6, 18, 26, 76, 50, which do not form a clear sequence. Let us check the numbers as products of consecutive integers: 6 is 2 times 3, 12 is 3 times 4, 30 is 5 times 6, 56 is 7 times 8, 132 is 11 times 12, and 182 is 13 times 14. The first factors are consecutive prime numbers: 2, 3, 5, 7, 11, 13. The next prime number is 17, so the next term is 17 times 18, which equals 306.

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