Let `a_(1),a_(2),a_(3),...` be a G `P` such that `a_(1)lt 0,a_(1)+a_(2)=4` and `a_(3)+a_(4)=16.` If `sum_(i=1)^(9)a_(i)=4 lambda`, then `lambda` is equal to

If a_(1),a_(2),a_(3),...,a_(100) are in A P such that a_(1)+a_(3)+a_(4)+a_(3)+a_(7)=20 then a_(4)=

Let {a_(n)} bc a G.P.such that (a_(4))/(a_(6))=(1)/(4) and a_(2)+a_(5)=216. Then a_(1)=

Let a_(1),a_(2)…,a_(n) be a non-negative real numbers such that a_(1)+a_(2)+…+a_(n)=m and let S=sum_(iltj) a_(i)a_(j) , then

Consider an A.P*a_(1),a_(2),a_(3),.... such that a_(3)+a_(5)+a_(8)=11 and a_(4)+a_(2)=-2 then the value of a_(1)+a_(6)+a_(7) is....

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

Let a_(1),a_(2),a_(3),...... be an A.P.such that (a_(1)+a_(2)+......+a_(p))/(a_(1)+a_(2)+a_(3)+......+a_(q))=(p^(3))/(q^(3));p!=q Then (a_(6))/(a_(21)) is equal to:

If a_(1),a_(2),a_(3),".....",a_(n) are in HP, than prove that a_(1)a_(2)+a_(2)a_(3)+a_(3)a_(4)+"....."+a_(n-1)a_(n)=(n-1)a_(1)a_(n)

The sequence a_(1),a_(2),a_(3),a_(4)...... satisfies a_(1)=1,a_(2)=2 and a_(n+2)=(2)/(a_(n+1))+a_(n),n=1,2,3... If 2^(lambda)a_(2012)=(2011!)/((1005!)^(2)) then lambda is equal to