Let `a_(1) ,a_(2),cdots , a_(n)` be an A.P. with common difference `pi//6` and assume
sec`a_(1) ` sec `a_(2)+sec a_(2) sec a_(3) + cdots + sec a_(n-1)` sec `a_(n)=k`
( tan `a_(n) - "tan" a_(1)`) Then find the value of k.

If a_1,a_2,…………..a_n are in AP with common difference d ne 0 then find (sin d) [sec a_1 sec a_2+ sec a_2 sec a_3+…….+sec a_(n-1) sec a_n]

If a_(n+1)= (1)/(1-a_(n)) for n gt=1 and a_(3) = a_(1) then find the value of (a_(2001))^(2001) .

Let {a_(n)} (n gt= 1 ) be a sequence such that a_(1) = 1 and 3a_(n+1)-3a_(n)=1 for all n gt= 1 . Then find the value of a_(2002) .

If a_(1) , a_(2), a_(3) , cdots ,a_(n) are in A.P. with a_(1) =3, a_(n) =39 and a_(1) +a_(2) + cdots +a_(n) =210 then the value of n is equal to

Let (1+x)^(n) = 1+a_(1)x + a_(2)x^(2) + ……+ a_(n)x^(n) . If a_(1), a_(2) and a_(3) are in AP, then the value of n is

Let a_(1) ,a_(2) ,a_(3) ,cdots ,a_(n) are in A.P such that a_(n) =100 , a_(10)- a_(39 ) = (3)/(5) then find the 15^(th) term of A.P. from end.

If a_(1), a_(2), a_(3),…….,a_(20) are in AP and a_(1) + a_(20) = 45 , then a_(1) + a_(2) + a_(3)+……+a_(20) is equal to

If a_1 = 4 and a_(n+1) = a_(n) + 4n for n ge 1 , then the value of a_(100) is

Let a_(1), a_(2),a_(3), cdots , a_(4001) are in A.P. such that (1)/(a_(1)a_(2))+(1)/(a_(2)a_(3))+ cdots + (1)/(a_(4000) a_(4001))= 10 and a_(2)+ a_(4000) = 50 then find the value of |a_(1)-a_(4001)| .

If a_(1), a_(2), a_(3), ………., a_(n) are in AP with common difference 5 and if a_(i)a_(j) ne -1 for i, j = 1, 2, …….., n, then tan^(-1)((5)/(1+a_(1)a_(2))) + tan^(-1)((5)/(1+a_(2)a_(3))) +……..+ tan^(-1)((5)/(1+a_(n-1)a_(n))) is equal to a) tan^(-1)((5)/(1+a(n)a_(n-1))) b) tan^(-1)((5)/(1+a(n)a_(n))) c) tan^(-1)((5n-5)/(1+a(n)a_(n+1))) d) tan^(-1)((5n-5)/(1+a_(1)a_(n)))