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 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 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 2Consider the arithmetic progression 3, 7, 11, ..... and let Aₙ denote the sum of the first n terms of this progression. Then the value of 125∑n=125An\frac{1}{25} \sum_{n=1}^{25} A_n251∑n=125An is