If `a , a_(1) , a_(2) ,a_(3) , cdots a_(2n), b` are in A.P. and `a, g_(1) , g_(2) , g_(3) , cdots , g_(2n), b` are in G.P. and h is the H.M of a and b then prove that
`(a_(1)+a_(2n))/(g_(1)g_(2n))+(a_(2)+a_(2n-1))/(g_(2)g_(2n-1))+cdots+ (a_(n)+a_(n+1))/(g_(n)g_(n+1))=(2n)/(h)`

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 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), a_(2),a_(3), cdots , 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))+cdots+ (a_(n+_2)-a_(n))/(a_(n+2)+a_(n)) is equal to

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)| .

Let a_(1),a_(2),a_(3),a_(4) and a_(5) be such that a_(1), a_(2) and a_(3) are in A.P. a_(2) ,a_(3) and a_(4) are in G.P and a_(3) ,a_(4) and a_(5) are in H.P . Then a_(1) ,a_(3) and a_(5) are in

If a_(1), a_(2), a_(3),….,a_(n) are in AP and a_(1) = 0 , then the value of ((a_(3))/(a_(2)) + (a_(4))/(a_(3)) +...+(a_(n))/a_(n-1))-a_(2) ((1)/(a_(2)) + (1)/(a_(3))+...+(1)/(a_(n-2))) is equal to a) (n-2) + (1)/((n-2)) b) (1)/((n-2)) c)(n - 2) d)(n - 1)

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

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)))