Question 390411: The first 15 letters of the following pattern are given. If this pattern were to be continued, what would the 100th letter?
A B B C C C D D D D E E E E E ...
Found 2 solutions by haileytucki, richard1234:
Answer by haileytucki(390)   (Show Source):
You can put this solution on YOUR website! Work the problem, adding a letter each time.
a bb ccc dddd eeeee
ffffff ggggggg hhhhhhhh
iiiiiiiii jjjjjjjjjj
kkkkkkkkkkk lllllllll111
mmmmmmmmmmmmm nnnnnnnnnnnnnn
N would be your 100th letter
Answer by richard1234(7193)  (Show Source):
You can put this solution on YOUR website! Instead of listing all 100 letters, we can notice that there is 1 A, 2 B's, 3 C's, 4 D's, etc.
Note that 1+2+...+13 = 91 and 1+2+...+14 = 105. Since M and N are the 13th and 14th letters of the alphabet, we can say that there are 91 letters in the subsequence
A B B ...M M M (all M's included)
and 105 terms in
A B B ...N N N (all N's included)
This implies that the 92nd through 105th terms are all N, so the 100th term is N.
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