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

The series follows a pattern where each new segment adds the next letter of the alphabet to the previous segment. Segment 1: A (1 letter) Segment 2: AB (2 letters) Segment 3: ABC (3 letters) Segment 4: ABCD (4 letters) ... and so on. To find the 100th letter, we need to determine which segment it falls into. We sum the lengths of the segments: Sum of lengths of 'n' segments = 1 + 2 + 3 + ... + n = n*(n+1)/2 Let's find 'n' such that the sum is close to 100: For n = 13: Sum = 13 * (13+1) / 2 = 13 * 14 / 2 = 13 * 7 = 91. This means after the 13th segment (ABC...M), 91 letters have appeared. For n = 14: Sum = 14 * (14+1) / 2 = 14 * 15 / 2 = 7 * 15 = 105. This tells us the 100th letter is within the 14th segment. The first 91 letters complete the first 13 segments. The 100th letter is (100 - 91) = 9 letters into the 14th segment. The 14th segment is "ABCD...N" (the first 14 letters of the alphabet). The 9th letter of the alphabet is I. Therefore, the 100th letter is I. The final answer is C) I.