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 2For a sequence of real numbers x1,x2,......xnx_1, x_2, ...... x_nx1,x2,......xn, if x1−x2+x3−....+(−1)n+1xn=n2+2nx_1 - x_2 + x_3 - .... + (-1)^{n + 1} x_n = n^2 + 2nx1−x2+x3−....+(−1)n+1xn=n2+2n for all natural numbers n, then the sum x49+x50x_{49} + x_{50}x49+x50 equalsCAT 2017 Slot 1Let a1,a2,……...a3na_{1}, a_{2}, \ldots \ldots . . . a_{3 n}a1,a2,……...a3n be an arithmetic progression with a1=3a_{1}=3a1=3 and a2=7a_{2}=7a2=7. If a1+a2+….+a3n=1830a_{1}+a_{2}+\ldots .+a_{3 n}=1830a1+a2+….+a3n=1830, then what is the smallest positive integer mmm such that m(a1+a2+….+an)>1830m\left(a_{1}+a_{2}+\ldots .+a_{n}\right)>1830m(a1+a2+….+an)>1830 ?CAT 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 be