Let a₁, a₂, a₃, be in an arithmetic progression of positive terms. Let A _ k = a ₁^2- a ₂^2+ a ₃^2- a ₄^2+ + a _ 2 k -1 ^2- a _ 2 k ^2 . If A ₃=-153, ~A ₅=-435 and a ₁^2+ a ₂^2+ a ₃^2=66 , then a ₁₇- A ₇ is equal to______

Step-by-step solution

aligned & d common diff. & A _ k =- kd [2 a +(2 k -1) d ] & A ₃=-153 & 153=13 ~d [2 a +5 ~d ] & 51= d [2 a +5 ~d ]...(1) & A ₅=-435 & 435=5 ~d [2 a +9 ~d ] & 87= d [2 a +9 ~d ] & (2)-(1) & 36=4 ~d ^2 & ~d =3, a =1 & a ₁₇- A ₇=49-[-7.3[2+39]]=910 aligned