What is the middle term of the sequence
Z, Z, Y, Y, Y, X, X, X, X, W, W, W, W, W, . . ., A ?
The correct answer is (A) H.
Explanation:
The sequence consists of letters from Z down to A, where each letter appears a number of times equal to its position counted backward from Z, or more simply, Z appears 2 times, Y appears 3 times, X appears 4 times, and so on down to A which appears 27 times (since A is the 26th letter from Z backwards, plus its own count). Let us calculate the total number of terms. The counts for each letter from Z to A are: 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, H=20, G=21, F=22, E=23, D=24, C=25, B=26, A=27. Total terms = sum of integers from 2 to 27 = (27 × 28)/2 - 1 = 378 - 1 = 377 terms. The middle term is the position (377 + 1)/2 = 189th term. Summing the frequencies 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). Sum up to K: 2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17 = 152. Next letter is J, which appears 18 times (from position 153 to 170). Next letter is I, which appears 19 times (from position 171 to 189). Thus, the 189th term falls right at the end of the letter I block. Therefore, the middle term is J.
हिंदी में प्रश्न एवं आदर्श उत्तर
अनुक्रम Z, Z, Y, Y, Y, X, X, X, X, W, W, W, W, W, ..., A का मध्य पद क्या है ?
सही उत्तर (A) H है।
व्याख्या:
The sequence consists of letters from Z down to A, where each letter appears a number of times equal to its position counted backward from Z, or more simply, Z appears 2 times, Y appears 3 times, X appears 4 times, and so on down to A which appears 27 times (since A is the 26th letter from Z backwards, plus its own count). Let us calculate the total number of terms. The counts for each letter from Z to A are: 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, H=20, G=21, F=22, E=23, D=24, C=25, B=26, A=27. Total terms = sum of integers from 2 to 27 = (27 × 28)/2 - 1 = 378 - 1 = 377 terms. The middle term is the position (377 + 1)/2 = 189th term. Summing the frequencies 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). Sum up to K: 2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17 = 152. Next letter is J, which appears 18 times (from position 153 to 170). Next letter is I, which appears 19 times (from position 171 to 189). Thus, the 189th term falls right at the end of the letter I block. Therefore, the middle term is J.