अनुक्रम
1, 1, 2, 1, 3, 2, 1, 4, 3, 2, 1, 5, 4, 3, 2, …
में प्रथम 28 पदों का योगफल क्या है?
Read this question in English
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 · (c) 85 · (d) 86
उत्तर और व्याख्या · explanation in English
Answer: (b) 84
After the first 1, the sequence runs in blocks 1 | 2, 1 | 3, 2, 1 | 4, 3, 2, 1 | …. The first 28 terms are the lone 1, the full blocks up to 6 (21 terms, sum 56) and the first 6 terms of the block 7, 6, …, 1 (sum 27): 1 + 56 + 27 = 84.
- Group the terms: 1 | 1 | 2, 1 | 3, 2, 1 | 4, 3, 2, 1 | 5, 4, 3, 2, 1 | …; after the first 1, block k is k, k − 1, …, 1.
- Blocks 1 to 6 have 1 + 2 + 3 + 4 + 5 + 6 = 21 terms; with the first 1 that makes 22 terms.
- Their sum = 1 + (1 + 3 + 6 + 10 + 15 + 21) = 1 + 56 = 57.
- Terms 23 to 28 are the first 6 terms of block 7: 7 + 6 + 5 + 4 + 3 + 2 = 27.
- Sum of the first 28 terms = 57 + 27 = 84.
Remember · In block sequences, count terms block by block (1, 2, 3, … terms) and handle the last, partial block separately.
Question and answer: UPSC's official GS Paper II (2024, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·