What is the middle term of the sequence Z, Z, Y, Y, Y, X, X, X, X, W, W, W, W, W,..., A?

The sequence follows a pattern where each letter, starting from Z, appears a certain number of times.

1. Identify the pattern: Z (1st letter from Z) appears 2 times. Y (2nd letter from Z) appears 3 times. X (3rd letter from Z) appears 4 times. ... A (26th letter from Z) appears 27 times. In general, the k-th letter from Z appears (k+1) times.

2. Calculate the total number of terms in the sequence: The total number of terms is the sum of (k+1) for k from 1 to 26. Sum = 2 + 3 + 4 + ... + 27. This is an arithmetic series with 26 terms. Total terms = (Number of terms / 2) * (First term + Last term) Total terms = (26 / 2) * (2 + 27) = 13 * 29 = 377.

3. Find the position of the middle term: Since the total number of terms (377) is odd, the middle term is at position (Total terms + 1) / 2. Middle term position = (377 + 1) / 2 = 378 / 2 = 189.

4. Determine the letter at the 189th position by summing the counts: Z: 2 terms (cumulative sum: 2) Y: 3 terms (cumulative sum: 2+3=5) X: 4 terms (cumulative sum: 5+4=9) W: 5 terms (cumulative sum: 9+5=14) V: 6 terms (cumulative sum: 14+6=20) U: 7 terms (cumulative sum: 20+7=27) T: 8 terms (cumulative sum: 27+8=35) S: 9 terms (cumulative sum: 35+9=44) R: 10 terms (cumulative sum: 44+10=54) Q: 11 terms (cumulative sum: 54+11=65) P: 12 terms (cumulative sum: 65+12=77) O: 13 terms (cumulative sum: 77+13=90) N: 14 terms (cumulative sum: 90+14=104) M: 15 terms (cumulative sum: 104+15=119) L: 16 terms (cumulative sum: 119+16=135) K: 17 terms (cumulative sum: 135+17=152) J: 18 terms (cumulative sum: 152+18=170) I: 19 terms (cumulative sum: 170+19=189)

   The 189th term falls within the block of 'I's, specifically it is the last 'I' in the sequence.

Therefore, the middle term of the sequence is I.

The final answer is B