If `A,A_(2),...,A_(n)` is a regular polygon.Then the vector `bar(A_(1)A_(2))+bar(A_(2)A_(3))+....+bar(A_(n)A)` ,is equal to

Let A_(1),A_(2),...A_(n) be the vertices of an n-sided regular polygon such that,(1)/(A_(1)A_(2))=(1)/(A_(1)A_(3))+(1)/(A_(1)A_(4)). Find the value of n.

If a_(1),a_(2),...a_(n) are in H.P then the expression a_(1)a_(2)+a_(2)a_(3)+...+a_(n-1)a_(n) is equal to

Let A_(1), A_(2), A_(3),…,A_(n) be the vertices of an n-sided regular polygon such that (1)/(A_(1)A_(2))=(1)/(A_(1)A_(3))+(1)/(A_(1)A_(4)). Find the value of n. Prove or disprove the converse of this result.

. 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_(3),.....a_(n) are in H.P.and a_(1)a_(2)+a_(2)a_(3)+a_(3)a_(4)+......a_(n-1)a_(n)=ka_(1)a_(n) then k is equal to

Let A_(1),A_(2),A_(3),.........,A_(14) be a regular polygon with 14 sides inscribed in a circle of radius R. If (A_(1)A_(3))^(2)+(A_(1)A_(7))^(2)+(A_(3)A_(7))^(2)=KR^(2) , then K is equal to :

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_(1),a_(2)...a_(n) are nth roots of unity then (1)/(1-a_(1))+(1)/(1-a_(2))+(1)/(1-a_(3))..+(1)/(1-a_(n)) is equal to