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 2020 Slot 3If x1=−1x_1 = -1x1=−1 and xm=xm+1+(m+1)x_m = x_{m+1} + (m + 1)xm=xm+1+(m+1) for every positive integer m,m,m, then x100x_{100}x100 equalsCAT 2017 Slot 2An infinite geometric progression a1,a2,a3,...a_1, a_2, a_3,...a1,a2,a3,... has the property that an=3(an+1+an+2+....)a_n = 3(a_{n+1} + a_{n+2} +....)an=3(an+1+an+2+....) for every n≥1n \ge 1n≥1. If the sum a1+a2+a3+.....=32a_1 + a_2 + a_3 +..... = 32a1+a2+a3+.....=32, then a5a_5a5 is