Correct Option (C)

The given sequence is 1, 3, 6, 11, 18, X, 42.

To determine the value of X, analyze the differences between consecutive terms:

3 - 1 = 2
6 - 3 = 3
11 - 6 = 5
18 - 11 = 7

The observed differences (2, 3, 5, 7) constitute a sequence of consecutive prime numbers. Following this pattern, the next prime number after 7 is 11.

Therefore, X is calculated by adding this prime number to the preceding term:

X = 18 + 11 = 29

To verify the pattern, the difference between the subsequent term (42) and X should be the next prime number after 11, which is 13:

42 - 29 = 13

This confirms that X = 29 maintains the established prime number difference pattern.

Incorrect Options:

If X were 26 (Option A), the difference between 18 and X would be 26 - 18 = 8. This does not follow the prime number sequence (2, 3, 5, 7, ...), as 8 is not a prime number and breaks the established pattern.

If X were 27 (Option B), the difference between 18 and X would be 27 - 18 = 9. This also deviates from the prime number sequence, as 9 is not a prime number.

If X were 30 (Option D), the difference between 18 and X would be 30 - 18 = 12. This does not align with the prime number sequence, as 12 is not a prime number.