If `sum_(j=1)^(21)a_(j)=693` ,where `a_(1),a_(2),......,a_(21)` are in AP., then `sum_(i=0)^(10)a_(2i+1)` is...

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 a_(1),a_(2),a_(3),a_(4) are in HP, then (1)/(a_(1)a_(4))sum_(r=1)^(3)a_(r)a_(r+1) is root of :

Assertion: Given that prod_(i=1)^(n)a_(i)=1 where a_(1),a_(2),a_(3)a_(i)in R then minimum value of sum_(i=1)^(n)a_(i) integrs is greater than or equal to their geometric mean.

If a_(1),a_(2),a_(3),......,a_(n) are in A.P. Where a_(k)>0AA K and sum_(K=2)^(n)(1)/(sqrt(a_(K-1))+sqrt(a_(K)))=(L)/(sqrt(a_(1))+sqrt(a_(n))) then L=

Let a_(1),a_(2),a_(3),"......"a_(10) are in GP with a_(51)=25 and sum_(i=1)^(101)a_(i)=125 " than the value of " sum_(i=1)^(101)((1)/(a_(i))) equals.

If A_(1),A_(2),A_(3)............ are in A.P., then sum_(i=1)^(2n)(-1)((A_(1)+A_(i+1))/(A_(i)-A_(i+1))) is equal to lambda n then | lambda| is equal to

If n>=3 and a_(1),a_(2),a_(3),.....,a_(n-1) are n^(th) roots of unity,then the sum of sum_(1<=i

If a_(1),a_(2),a_(3),....,a_(4001) are terms of AP such that sum_(i=1)^(4000)(1)/(a_(i)a_(i+1))=108a_(2)+a_(4000)=50 then |a_(1)-a_(4000)|=

Let a_(1),a_(2),a_(3),...,a_(101) are in G.P.with a_(101)=25 and sum_(i=1)^(201)a_(1)=625. Then the value of sum_(i=1)^(201)(1)/(a_(1)) equals

If a_(1),a_(2),a_(3), . .. . ,a_(n) are in A.P. and a_(i)gt0 for each i=1,2,3, . . ..,n, then sum_(r=1)^(n-1)(1)/(a_(r+1)^(2//3)+a_(r+1)^(2//3)a_(r)^(1//3)+a_(r)^(1//3)) is equal to