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

1. A. H
2. B. I
3. C. J
4. D. M

Answer: B

Explanation

The sequence consists of letters of the alphabet, where each letter appears a number of times equal to (28 – its position in the alphabet from A). So, Z (26th letter) appears 2 times, Y (25th) appears 3 times, …, A (1st) appears 27 times. The total number of terms in the sequence is the sum 2 + 3 + 4 + … + 27. This is an arithmetic series sum: (number of terms / 2) * (first term + last term) = (26/2) * (2 + 27) = 13 * 29 = 377. The middle term is (377 + 1) / 2 = 189th term. To find the 189th term, we sum the occurrences from Z downwards: Z (2), Y (3), X (4), W (5), V (6), U (7), T (8), S (9), R (10), Q (11), P (12), O (13), N (14), M (15), L (16), K (17), J (18), I (19). Summing these: 2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18 = 170. The next letter is ‘I’, which appears 19 times. The 189th term falls within the ‘I’ block (171st to 189th term). Thus, the middle term is I.