What is the sum of the first 28 terms in the following sequence? 1, 1, 2, 1, 3, 2, 1, 4, 3, 2, 1, 5, 4, 3, 2, …
- (a) 83
- (b) 84 ✓ UPSC's answer
- (c) 85
- (d) 86
Why the answer is (b)
• The sequence is made of blocks that count down: (1), (2, 1), (3, 2, 1), (4, 3, 2, 1), …
• Block n has n terms, so the first 7 blocks contain 1 + 2 + … + 7 = 28 terms — exactly the first 28 terms.
• Each block sums to 1 + 2 + … + n: the block sums are 1, 3, 6, 10, 15, 21, 28.
• Total = 1 + 3 + 6 + 10 + 15 + 21 + 28 = 84 — option (b).
Why the other options are wrong
- (a) 83
- 83 is incorrect because the exact sum of the first 7 blocks is 84, not 83.
- (c) 85
- 85 is incorrect because the exact sum of the first 7 blocks is 84, not 85.
- (d) 86
- 86 is incorrect because the exact sum of the first 7 blocks is 84, not 86.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2024, held on 16 June 2024. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.