What is X in the sequence 1, 3, 6, 11, 18, X, 42?

1. **Analyze the Gaps (Method of Differences):** First, we find the difference between the given numbers [21]:\n - $3 - 1 = 2$\n - $6 - 3 = 3$\n - $11 - 6 = 5$\n - $18 - 11 = 7$\n\n2. **Identify the Pattern:** The differences are **2, 3, 5, 7**. \n - A crucial observation is that **2 is the only even prime number** [34]. This tells us the pattern is *not* odd numbers (1, 3, 5...), but rather **Prime Numbers** [29].\n\n3. **Apply the Pattern:** The next number in the prime sequence after 7 is **11**.\n - Therefore, $X = 18 + 11 = 29$.\n\n4. **Verify with End-Term:** We must ensure this pattern fits the final number, 42 [46].\n - The prime number after 11 is **13**.\n - Does $29 + 13$ equal 42? Yes, it does.\n - This 'End-Term Verification' confirms our logic is correct [53].\n\n**Conclusion:** The missing number is 29.