abbcccddddeeeee........... what will be the 126th digit?

Question

abbcccddddeeeee........... what will be the 126th digit?

Answer 1

This is related to the problem:

 

How many terms will it take for the sum 1 + 2 + 3 + … + n to be greater than 126?

 

The sum of the first n positive integers is n(n+1)/2. Set this equal to 126 and solve for n:

 

n(n+1)/2 = 126

 

n² + n - 252 = 0

 

n = -16.38 or n = 15.38  (these are approximations found from the quadratic formula)

 

This means that when n = 15 (which corresponds to the letter O, there will be a string of fifteen O's. After them the next letter will be a P. The last O is in the 120th position in the string, so the 126th letter must be a P.