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 2017 Slot 1If the square of the 777th term of an arithmetic progression with positive common difference equals the product of the 333rd and 171717th terms, then the ratio of the first term to the common difference isCAT 2019 Slot 2If (2n+1)+(2n+3)+(2n+5)+....+(2n+47)=5280(2n + 1) + (2n + 3) + (2n + 5) + .... + (2n + 47) = 5280(2n+1)+(2n+3)+(2n+5)+....+(2n+47)=5280, then what is the value of 1+2+3+...+n1 + 2 + 3 + ... + n1+2+3+...+n?CAT 2024 Slot 3Consider the sequence t1=1t_1 = 1t1=1, t2=−1t_2 = -1t2=−1 and tn=(n−3n−1)tn−2t_n = \left(\frac{n-3}{n-1}\right) t_{n-2}tn=(n−1n−3)tn−2 for n≥3n \ge 3n≥3. The, the value of the sum 1t2+1t4+1t6+⋯+1t2022+1t2024\frac{1}{t_2} + \frac{1}{t_4} + \frac{1}{t_6} + \dots + \frac{1}{t_{2022}} + \frac{1}{t_{2024}}t21+t41+t61+⋯+t20221+t20241 is