What is the middle term of the sequence Z, Z, Y, Y, Y, X, X, X, X, W, W, W, W, W,..., A ?
This questions was previously asked in
Complete-Test, Previous year (2023)
Explanation:
- Let’s decode the pattern:
- 2 Zs, 3 Ys, 4 Xs, 5 Ws …
- The nth letter from the end repeats (n+1) times.
- The sequence goes from Z to A, each getting one more repeat than before.
- To find the middle term, count the total terms:
- Sequence starts at Z (position 26), continues down to A (position 1).
- Total terms = 2 (Z) + 3 (Y) + 4 (X) + ... + 27 (A)
- This is a series: 2 + 3 + ... + 27
- Total terms = (2 + 27) × 26 / 2 = 29 × 13 = 377
- The middle term is at position 189 (since 377/2 = 188.5, so 189th term).
- Now, sum the counts till reaching 189 to know which letter it is:
- Z: 2 terms (1-2)
- Y: 3 terms (3-5)
- X: 4 terms (6-9)
- W: 5 terms (10-14)
- ...
- The general count for nth letter: Number of terms till nth letter from last (Z is 1st from end) is:
S = sum_{k=2}^{n} k = (n(n+1)/2) - 1
- Let's find n where cumulative becomes >= 189.
- Try n = 18:
S = 18 × 19 / 2 - 1 = 171 - 1 = 170
- Next, n = 19:
S = 19 × 20 / 2 - 1 = 190 - 1 = 189
- So, the 189th term is at the completion of the 19th letter from end, i.e., on letter "I".
- Options:
1. H
2. I
3. J
4. M
- Correct answer is option: 2 - I
By: sunny bhonsle ProfileResourcesReport error