CATAlgebra > Hardn−1a1+an\frac{n-1}{\sqrt{a_{1}}+\sqrt{a_{n}}}a1+ann−1na1−aa+1\frac{\mathrm{n}}{\sqrt{\mathrm{a}_{1}}-\sqrt{\mathrm{a}_{\mathrm{a}+1}}}a1−aa+1nn−1a1+a2−1\frac{n-1}{\sqrt{a_{1}}+\sqrt{a_{2-1}}}a1+a2−1n−1na1+an+1\frac{n}{\sqrt{a_{1}}+\sqrt{a_{n+1}}}a1+an+1n✅ Correct Option: 4Related questions:CAT 2022 Slot 2The average of a non-decreasing sequence of NNN numbers a1,a2,…,aNa_{1}, a_{2}, \ldots, a_{N}a1,a2,…,aN is 300300300. If a1a_{1}a1 is replaced by 6a16 a_{1}6a1, the new average becomes 400400400. Then, the number of possible values of a1a_{1}a1 isCAT 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 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, is