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

Answer: (b) I

Z appears 2 times, Y 3 times and so on, up to A 27 times, so there are 377 terms and the middle one is the 189th. The first k letters fill k(k + 3)/2 places; for k = 18 this is exactly 189, so the middle term is the 18th letter counted from Z, which is I.

1. The kth letter from Z appears k + 1 times: Z (2), Y (3), …, A (27).
2. Total terms = 2 + 3 + … + 27 = 377, so the middle term is the (377 + 1)/2 = 189th.
3. The first k letters take up 2 + 3 + … + (k + 1) = k(k + 3)/2 places.
4. k = 17 gives 170 and k = 18 gives 189, so the 189th term is the last copy of the 18th letter from Z.
5. Counting back from Z: Z, Y, X, W, V, U, T, S, R, Q, P, O, N, M, L, K, J, I — the 18th is I.

Remember · For blocks of growing length, find the total, locate the middle position, then use running totals to see which block holds it.

Question and answer: UPSC's official GS Paper II (2023, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). · Report an error