CATAlgebra > Mediumy,x\mathrm{y}, \mathrm{x}y,x and z are in arithmetic progressionx,yx, \mathrm{y}x,y and zzz are in geometric progressionx,z\sqrt{\mathrm{x}}, \sqrt{\mathrm{z}}x,z and y\sqrt{\mathrm{y}}y are in arithmetic progressionx,z\sqrt{\mathrm{x}}, \sqrt{\mathrm{z}}x,z and z\sqrt{\mathrm{z}}z are in arithmetic progression✅ Correct Option: 1Related 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 2019 Slot 1If the population of a town is ppp in the beginning of any year then it becomes 3+2p3+2 p3+2p in the beginning of the next year. If the population in the beginning of 201920192019 is 100010001000 then the population in the beginning of 203420342034 will beCAT 2022 Slot 1For any natural number n, suppose the sum of the first n terms of an arithmetic progression is (n+2n2)(n + 2n^2)(n+2n2). If the nthn^{th}nth term of the progression is divisible by 999, then the smallest possible value of nnn is