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What should come in place of '?' in the given series? 12 18 30 42 66 ?
78
84
90
96
78
Observe that the series represents the product of prime numbers and the multiplier 6 (6x2, 6x3, 6x5, 6x7, 6x11, 6x13).
Observe that the series represents the product of prime numbers and the multiplier 6 (6x2, 6x3, 6x5, 6x7, 6x11, 6x13).
Analyze the difference between terms
Calculate the differences between consecutive terms: 18-12=6, 30-18=12, 42-30=12, 66-42=24. This pattern is not constant.
Identify the multiplication pattern
Express each number as a multiple of 6: 12=(62), 18=(63), 30=(65), 42=(67), 66=(6*11). The multipliers are prime numbers: 2, 3, 5, 7, 11.
Calculate the next term
The next prime number after 11 is 13. Therefore, the missing term is 6 * 13 = 78.
B: 84 is incorrect as it would require the multiplier 14, which is not prime; C: 90 is incorrect as it follows no logical progression in this prime sequence; D: 96 is incorrect as 96/6 = 16, which is not a prime number.
A is correct because the series follows the pattern of 6 multiplied by consecutive prime numbers 2, 3, 5, 7, 11, and the next prime is 13, resulting in 6*13 = 78.
When a series jumps by non-uniform increments, always check for prime number relationships or multiplications by constant factors.
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