Q. In the series AABABCABCDABCDE..., which letter occupies the 100th position? (UPSC Prelims 2008)
Answer: I
Notes: The series is formed of blocks where the k-th block has length k and consists of the first k letters starting from A. The total length up to block k is k(k+1)/2. For position 100, find k such that T_k ≥ 100. T_13 = 91 and T_14 = 105, so position 100 lies in block 14. The offset in this block is 100 - 91 = 9, which corresponds to the 9th letter starting from A: A(1), B(2), ..., I(9). Thus, the letter at position 100 is I, option (b).