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

In the series AABABCABCDABCDE.., which letter appears at the 100th place?
  1. G
  2. H
  3. I
  4. J

Solution

The pattern is groups: A, AB, ABC, ABCD, ABCDE, ... The nth group has n letters. Cumulative letters up to the 14th group = $(14/2)(1 + 14) = 105$. So the 14th group occupies positions 92 to 105 and is ABCDEFGHIJKLMN. The 100th position is the 9th letter of this group, which is I.

Asked in: CSAT 2022

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