1,2,4,12,60,()

2025-09-02 阅读 81 评论 0

摘要：To determine the next number in the sequence (1, 2, 4, 12, 60, ldots), we *yzed two potential pat

To determine the next number in the sequence (1, 2, 4, 12, 60, ldots), we *yzed two potential patterns: a multiplicative pattern using primes and an additive pattern using double factorials.

1,2,4,12,60,()

1. Multiplicative Pattern with Primes:

The sequence starts with 1.

Each subsequent term is obtained by multiplying the previous term by a prime number, starting with 2, then repeating 2, followed by 3, 5, etc.

The multipliers are 2, 2, 3, 5, which are primes except for the first two terms.

Following this pattern, the next multiplier is 7.

Calculation: (60 imes 7 = 420).

2. Additive Pattern with Double Factorials:

The differences between consecutive terms are 1, 2, 8, 48.

These differences correspond to double factorials of even numbers: (0!! = 1), (2!! = 2), (4!! = 8), (6!! = 48).

The next difference is (8!! = 384).

Calculation: (60 + 384 = 444).

After considering both patterns, the multiplicative pattern using primes is more straightforward and commonly expected in such problems. The sequence multipliers are primes starting with 2, repeated once, followed by subsequent primes.

Thus, the next number in the sequence is (boxed{420}).

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