Multiple Choice Questions on What is the middle term of the sequence Z Z Y Y Y X X X X W W W W W A ........ for Civil Services Exam (CSAT) Preparation

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    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)

    H

    Incorrect Answer

    I

    Correct Answer

    J

    Incorrect Answer

    M

    Incorrect Answer
    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


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