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 2020 Slot 2Let the mthm^{th}mth and nthn^{th}nth terms of a geometric progression be 3/43 / 43/4 and 121212, respectively, where m<nm<nm<n. If the common ratio of the progression is an integer rrr, then the smallest possible value of r+n−mr+n-mr+n−m isCAT 2022 Slot 1For any natural number n, suppose the sum of the first n terms of an arithmetic progression is (n+2n2)(n + 2n^2)(n+2n2). If the nthn^{th}nth term of the progression is divisible by 999, then the smallest possible value of nnn isCAT 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 is