Find the sum of first 24 terms of the A.P `a_(1) , a_(2) , a_(3) , cdots ,` if it is known that `a_(1) +a_(5)+a_(10)+a_(15)+ a_(20)+a_(24)` =225.

Find minors and cofactors of the elements a_(11), a_(21) in the determinant Delta=|[a_(11), a_(12 ), a_(13)], [a_(21), a_(22), a_(23)],[ a_(31) , a_(32), a_(33)]|

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_(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

If a_(1), a_(2), …, a_(50) are in GP, then " "(a_(1)-a_(3)+a_(5)-…+a_(49))/(a_(2)-a_(4)+a_(6)-…+a_(50)) is equal to :

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.

Find the minors and cofactors of a_(11), a_(1 2) and a_(13) of the matrix A=[[1, -1, 3],[ 2, 2, -1],[ -1, 3, 5]]

Three distinct A.P. s' have same first term common differences as d_(1) ,d_(2) ,d_(3) and n^(th) terms as a_(n) , b_(n) ,c_(n) respectively such that (a_(1))/(d_(1))=(2b_(1))/(d_(2))=(3c_(1))/(d_(3)). If (a_(7))/(c_(6))=(3)/(7) then find the value of (b_(7))/(c_(6)) .

If Delta=|[a_(11), a_(12 ), a_(13)], [a_(21), a_(22), a_(23)],[ a_(31) , a_(32), a_(33)]| and A_(i j) is cofactors of a_(ij) , then value of Delta is given by i) a_(11) A_(31)+a_(12) A_(32)+a_(13) A_(33) ii) a_(11) A_(11)+a_(12) A_(21)+a_(13) A_(31) iii) a_(21) A_(11)+a_(22) A_(12)+a_(23) A_(13) iv) a_(11) A_(11)+a_(21) A_(21)+a_(31) A_(31)