In the series AABABCABCDABCDE..., which letter appears at the 100th place?

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.

1. Split the series into blocks: A | AB | ABC | ABCD | ABCDE | … The nth block runs from A to the nth letter and has n letters.
2. Places used by the first n blocks = 1 + 2 + … + n = n(n + 1)/2. For n = 13 this is 13 × 14 ÷ 2 = 91.
3. So the 100th place is the 100 − 91 = 9th letter of the 14th block (A to N).
4. The 9th letter of the alphabet is I.
5. 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). · Report an error