Let x ₁, x ₂, x ₃, x ₄ be in a geometric progression. 2,7,9,5 are subtracted respectively from x₁, x₂, x₃x₄ then the resulting numbers are in an arithmetic progression. Then the value of 1 24 (x₁ x₂ x₃ x₄ ) is :

Step-by-step solution

x ₁, x ₂, x ₃, x ₄ G.P. Let a, ar, ar ^2, ar ^3 G.P. Now a-2, a r-7, a^2-9, ar ^3-5 A.P. 2( ar -7)= a -2+ ar ^2-9 ....(i) 2 ( ar ^2-9 )= ar -7+ ar ^3-5 ....(ii) aligned & Solving r =2, a =-3 & Product = x ₁, x ₂, x ₃, x ₄= a ^4 r ^6=81 64 aligned aligned & Solving r =2, a =-3 & Product = x ₁, x ₂, x ₃, x ₄= a ^4 r ^6=81 64 aligned