Explanation:

The given series is: AABABCABCDABCDE…
The pattern being followed here is: A, AB, ABC, ABCD, ABCDE, …
It’s kind of an arithmetic series wherein the first term has 1 letter, second term has 2 letters, and so on. We have to estimate the length of the letter-series near the 100th letter.
If we have an arithmetic series, 1, 2, 3 …, then:
Sum of first n terms = (n/2) (a + l), where ‘n’ is the number of terms in the series, ‘a’ the first term, and ‘l’ the last term.
So, sum of first 14 terms = (14/2) (1 + 14) = 7 × 15 = 105
So, the term having 14 letters will have the 100th letter of the series.
It will start at the 92nd letter and end at 105th letter. Hence, the 100th letter must be I.