SOLUTION: 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 ...

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.
RELATED QUESTIONS
If the letters of the alphabet are in the following pattern abbcccddddeeeee... and it... (answered by brucewill)
if the pattern of the first 4 letters of MATHMATHMATH...continures to the right, the 1234 (answered by stanbon)
The pattern of the first 7 letters of contestcontestcontest...continues to the right. The (answered by Edwin McCravy)
3, 10, 17, 24, ... If the number pattern above continues, what will be the 100th number... (answered by brysca,MathTherapy)
There are 10 blocks on the diagram. The first, fifth, and 9th are shaded. If the pattern... (answered by solver91311)
There are 10 blocks on the diagram. The first, fifth, and 9th are shaded. If the pattern... (answered by macston)
examine the following phrase famous by fred flintstone: yabbadabbadoo. if this pattern is (answered by AnlytcPhil)
examine the following phrase famous by fred flintstone: yabbadabbadoo. if this pattern is (answered by Alan3354)
The sequence of the numbers are: -15, -11, -7, -3, what is the formula for this pattern?... (answered by josgarithmetic)