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 2023 Slot 2Let both the series a1,a2,a3,…a_1, a_2, a_3, \dotsa1,a2,a3,… and b1,b2,b3…b_1, b_2, b_3 \dotsb1,b2,b3… be in arithmetic progression such that the common differences of both the series are prime numbers. If a5=b9a_5 = b_9a5=b9, a19=b19a_{19} = b_{19}a19=b19 and b2=0b_2 = 0b2=0, then a11a_{11}a11 equalsCAT 2018 Slot 2Let t1,t2,…t_1, t_2, \dotst1,t2,… be real numbers such that t1+t2+⋯+tn=2n2+9n+13t_1 + t_2 +\dots+ t_n = 2n^2 + 9n + 13t1+t2+⋯+tn=2n2+9n+13, for every positive integer n≥2n\ge2n≥2. If tk=103t_k =103tk=103, then kkk equalsCAT 2024 Slot 1Suppose x1,x2,x3,…,x100x_{1}, x_{2}, x_{3}, \ldots, x_{100}x1,x2,x3,…,x100 are in arithmetic progression such that x5=−4x_{5}=-4x5=−4 and 2x6+2x9=x11+x132 x_{6}+2 x_{9}=x_{11}+x_{13}2x6+2x9=x11+x13, Then, x100x_{100}x100 equals