CATAlgebra > Medium−5150-5150−5150−5051-5051−5051−5050-5050−5050−5151-5151−5151✅ Correct Option: 3Related questions:CAT 2023 Slot 1For some positive and distinct real numbers x,yx, yx,y and zzz, if 1y+z\frac{1}{\sqrt{y}+\sqrt{z}}y+z1 is the arithmetic mean of 1x+z\frac{1}{\sqrt{x}+\sqrt{z}}x+z1 and 1x+y\frac{1}{\sqrt{x}+\sqrt{y}}x+y1, then the relationship which will always hold true, isCAT 2018 Slot 2The value of the sum 7×11+11×15+15×19+⋯+95×997 \times 11 + 11 \times 15 + 15 \times 19 + \dots + 95 \times 997×11+11×15+15×19+⋯+95×99 isCAT 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