CATAlgebra > Medium415415415442442442455455455404404404✅ Correct Option: 3Related questions:CAT 2019 Slot 2Let a1,a2,...a_1, a_2, ...a1,a2,... be integers such that a1−a2+a3−a4+...+(−1)n−1an=na_1 - a_2 + a_3 - a_4 + ... + (-1)^{n - 1} a_n = na1−a2+a3−a4+...+(−1)n−1an=n, for all n≥1n \ge 1n≥1. Then a51+a52+...+a1023a_{51} + a_{52} + ... + a_{1023}a51+a52+...+a1023 equalsCAT 2021 Slot 3Consider a sequence of real number x1,x2,x3,...x_1, x_2, x_3, ...x1,x2,x3,... such that xn+1=xn+n−1x_{n+1} = x_n + n - 1xn+1=xn+n−1 for all n≥1n \ge 1n≥1. If x1=−1x_1 = -1x1=−1 then x100x_{100}x100 is equal toCAT 2021 Slot 1The natural numbers are divided into groups as (1), (2,3,4),(5,6,7,8,9),….(2,3,4),(5,6,7,8,9), \ldots .(2,3,4),(5,6,7,8,9),….. and so on. Then, the sum of the numbers in the 15th group is equal to