श्रेणी AABABCABCDABCDE... में 100वें स्थान पर कौन-सा वर्ण आएगा?
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In the series AABABCABCDABCDE..., which letter appears at the 100th place?
(a) G · (b) H · (c) I · (d) J
उत्तर और व्याख्या · explanation in English
Answer: (c) I
The series is built in blocks A | AB | ABC | ABCD | …, the nth block having n letters. The first 13 blocks use 91 places, so the 100th place is the 9th letter of the 14th block, which is I.
- Split the series into blocks: A | AB | ABC | ABCD | ABCDE | … The nth block runs from A to the nth letter and has n letters.
- Places used by the first n blocks = 1 + 2 + … + n = n(n + 1)/2. For n = 13 this is 13 × 14 ÷ 2 = 91.
- So the 100th place is the 100 − 91 = 9th letter of the 14th block (A to N).
- The 9th letter of the alphabet is I.
- Check: the 14th block ends at place 91 + 14 = 105, so place 100 does fall inside it.
Remember · Growing-block series: find the largest n with n(n + 1)/2 below the position; the remainder names the letter.
Question and answer: UPSC's official GS Paper II (2022, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·