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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.