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

(a) 26
(b) 27
(c) 29 ✓ UPSC's answer
(d) 30

Why the answer is (c)

• Calculate the differences between consecutive terms: 3-1=2, 6-3=3, 11-6=5, 18-11=7.

• Observe that the differences (2, 3, 5, 7) are consecutive prime numbers.

• The next prime number after 7 is 11.

• Add 11 to the previous term (18) to find X: 18 + 11 = 29.

• Verify the next term: The next prime is 13, and 29 + 13 = 42, which matches the sequence.

• Therefore, X is 29, corresponding to option (c).

Why the other options are wrong

(a) 26: 26 implies a difference of 8, which is not the next prime number in the sequence of differences.
(b) 27: 27 implies a difference of 9, which is not a prime number.
(d) 30: 30 implies a difference of 12, which is not the next prime number in the sequence of differences.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2025, held on 25 May 2025. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.