Let `x_(1),x_(2),x_(3),....` be terms of an AP, if `(x_(1)+x_(2)+...+x_(n))/(x_(1)+x_(2)+...+x_(m))=(n^(2))/(m^(2)).(n!=m)," then "(x_(8))/(x_(23))=?`

If x_(1),x_(2),x_(3)...x_(n) are in H.P,then prove that x_(1)x_(2)+x_(2)x_(3)+xx x-3x_(4)+...+x_(n-1)x_(n)=(n-1)x_(1)x_(n)

(m)/(n)x^(2)+(n)/(m)=1-2x

If x_(1)=2 and x_(n+1)=sqrt(x_(n)^(2)+8) , then x_(4)=

If x_(1), x_(2), x_(3) .................x_(n) are in H.P.then x_(1)x_(2)+x_(2)x_(3)+.......+x_(n-1)x_(n) =

If x_(1),x_(2),x_(3),"……" are in A.P., then the value of 1/(x_(1)x_(2))+1/(x_(2)x_(3))+1/(x_(3)x_(4))+"……"1/(x_(n-1)x_(n)) is :

If x_(1),x_(2),x_(3),......x2_(n) are in A.P, then sum_(r=1)^(2n)(-1)^(r+1)x_(r)^(2) is equal to

If x_(1), x_(2),"……….",x_(n) are n non zero real numbers such that (x_(1)^(2) + x_(2)^(2) + "...."+x_(n-1)^(2))( x_(2)^(2) + x_(3)^(2) + x_(3)^(2) + "......" + x_(n)^(2))le ( x_(1) x_(2) + x_(2) x_(3)+"....."+x_(n-1)x_(n))^(2) , then x_(1) , x_(2) ,".....",x_(n) are in :