if the series is given as a,b,b,c,c,c,d,d,d,d ....then which term will replicate u?

Question

(a)200

(b)210

(c)215

(d)229

(e)232

Answer 1

I posted a comment but it didn't show up so I'll explain it here.

The letter u is the 21st letter. S=21(21+1)/2=231 and 231-21=210, or t is the 20th letter and S=20(20+1)/2=210.

The last t is in position 210. The u's are in positions 211-231. This means that c) 215 and d) 229 are both correct.

Answer 2

(edited; THX to Arthur)
 
This problem assumes that you know Gauss’ Formula for the sum of the numbers from 1 to N:
              Sum = (N)*(N+1)/2

Let’s try an example:  The letter “d” is the 4th letter of the alphabet and the last “d” in the series is at position    (4)*(4+1)/2 = 10   (note: count the letters).

O.K., now the problem:
      The letter “u” is the 21st letter in the English alphabet.  So, there are 21 letter “u”’s in the series, the last of which is in position 21*22/2 = 231.  The letter “u” will be in positions 211-231.

Ouch!   This means that answers (c) and (d) are both correct.  You might point that out when giving your answer.