[" If "a_(1),a_(2),a_(3),...a_(2n)" are in A.P.then "],[a_(1)^(2)-a_(2)^(2)+a_(3)^(2)-a_(4)^(2)+....+a_(2n-1)^(2)-a_(2n)^(2)=]

If the sequence a_(1),a_(2),a_(3),…,a_(n) is an A.P., then prove that a_(1)^(2)-a_(2)^(2)+a_(3)^(2)-a_(4)^(2)+…+a_(2n-1)^(2)-a_(2n)^(2)=n/(2n-1)(a_(1)^(2)-a_(2n)^(2))

If the sequence a_(1),a_(2),a_(3),…,a_(n) is an A.P., then prove that a_(1)^(2)-a_(2)^(2)+a_(3)^(2)-a_(4)^(2)+…+a_(2n-1)^(2)-a_(2n)^(2)=n/(2n-1)(a_(1)^(2)-a_(2n)^(2))

If the sequence a_(1),a_(2),a_(3),…,a_(n) is an A.P., then prove that a_(1)^(2)-a_(2)^(2)+a_(3)^(2)-a_(4)^(2)+…+a_(2n-1)^(2)-a_(2n)^(2)=n/(2n-1)(a_(1)^(2)-a_(2n)^(2))

Let the sequence a_(1),a_(2),a_(3),...,a_(n) from an A.P.Then the value of a_(1)^(2)-a_(2)^(2)+a_(3)^(2)-...+a_(2n-1)^(2)-a_(2n)^(2) is (2n)/(n-1)(a_(2n)^(2)-a_(1)^(2))(b)(n)/(2n-1)(a_(1)^(2)-a_(2n)^(2))(n)/(n+1)(a_(1)^(2)-a_(2n)^(2))(d)(n)/(n-1)(a_(1)^(2)+a_(2n)^(2))

if a,A_(1),A_(2),A_(3)......,A_(2n),b are in A.P.then sum_(i=1)^(2n)A_(i)=(a+b)

If the sequence a_(1),a_(2),a_(3),dots a_(n),.... forms an A.P.then prove that a_(1)^(2)-a_(2)^(2)+a_(3)^(2)+...+a_(4)^(2)=(n)/(2n-1)(a_(1)^(2)-a_(2n)^(2))

If a_(1),a_(2),a_(3),...,a_(2n+1) are in A.P.then (a_(2n+1)-a_(1))/(a_(2n+1)+a_(1))+(a_(2n)-a_(2))/(a_(2n)+a_(2))+...+(a_(n+2)-a_(n))/(a_(n+2)+a_(n)) is equal to (n(n+1))/(2)xx(a_(2)-a_(1))/(a_(n+1)) b.(n(n+1))/(2) c.(n+1)(a_(2)-a_(1)) d.none of these

If a_(1),a_(2),a_(3),dots,a_(n+1) are in A.P.then (1)/(a_(1)a_(2))+(1)/(a_(2)a_(3))...+(1)/(a_(n)a_(n+1)) is

. If a_(1),a_(2),a_(3),...,a_(2n+1) are in AP then (a_(2n+1)+a_(1))+(a_(2n)+a_(2))+...+(a_(n+2)+a_(n)) is equal to

If a_(1), a_(2),…a_(n) are in H.P. then a_(1).a_(2) + a_(2).a_(3) + a_(3).a_(4) + …+ a_(n-1) .a_(n) =