Q. What is the middle term of the sequence
Z, Z, Y, Y, Y, X, X, X, X, W, W, W, W, W,…, A?
(a) H
(b) I
(c) J
(d) M
Correct Answer: (b) I
Question from UPSC Prelims 2023 CSAT
Explanation :
Middle term of the sequence
The given sequence is a pattern of letters from the English alphabet starting from Z and going backwards to A. Each letter is repeated a number of times equal to its position in the reversed alphabet (Z is 1st, Y is 2nd, X is 3rd, and so on).
The total number of terms in the sequence is calculated by adding the number of repetitions for each letter, which forms an arithmetic series: 2 (for Z) + 3 (for Y) + 4 (for X) + … + 27 (for A).
The sum of this series is 377= (n(n+1)/2 -1), n=27
The middle term is the 189th term (since 377/2 = 188.5). To find out which letter this term is, we subtract the total number of terms for the letters before it from 189.
The total number of terms for the letters before I (starting from Z) is 188 (2 for Z, 3 for Y, 4 for X, …, 8 for S). So, 189 – 188 = 1, which means the 189th term is the first repetition of I. Therefore,
The middle term of the sequence is I.
Proof – A+B+C+D+E+F+G+H=27+26+25+24+23+22+21+20=188
