Replace the incorrect term by the correct term in the given sequence 3, 2, 7, 4, 13, 10, 21, 18, 31, 28, 43, 40 where odd terms and even terms follow the same pattern.
- (a) 0 ✓ UPSC's answer
- (b) 1
- (c) 3
- (d) 6
Why the answer is (a)
• Odd-position terms: 3, 7, 13, 21, 31, 43 — differences 4, 6, 8, 10, 12.
• Even-position terms: 2, 4, 10, 18, 28, 40 — differences 2, 6, 8, 10, 12. To follow the same pattern the first difference must be 4, so the first even term should be 4 − 4 = 0.
• With 0 in place of 2, both halves read 0, 4, 10, 18, 28, 40 (differences 4, 6, 8, 10, 12), matching the odd terms' pattern.
• So the incorrect term 2 is replaced by 0, option (a).
Why the other options are wrong
- (b) 1
- With 1 in place of 2 the even terms would have differences 3, 6, 8…, still not matching 4, 6, 8….
- (c) 3
- 3 is already the first odd term; putting 3 among the even terms gives differences 1, 6, 8….
- (d) 6
- With 6 in place of 2 the differences would be −2, 6, 8…, which does not match.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2021, held on 10 October 2021. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.