If `a_(1),a_(2),a_(3),... a _(12)` are in `A.P.` with common difference equal to `((1)/(sqrt(2)))` then the value of `Delta=|[a_(1)a_(5),a_(1),a_(2)],[a_(2)a_(6),a_(2),a_(3)],[a_(3)a_(7),a_(3),a_(4)]|` is equal to

,1+a_(1),a_(2),a_(3)a_(1),1+a_(2),a_(3)a_(1),a_(2),1+a_(3)]|=0, then

If a_(0),a_(1),a_(3),a_(4)......... are in AP with common difference d where d!=0,1,-1, then the det[[a_(1)a_(2),a_(1),a_(0)a_(2)a_(3),a_(2),a_(1)a_(3)a_(4),a_(3),a_(2)]] is

If a_(1),a_(2),a_(3),a_(4),a_(5) are in HP, then a_(1)a_(2)+a_(2)a_(3)+a_(3)a_(4)+a_(4)a_(5) is eqiual to

" (iv) "|[1+a_(1),a_(2),a_(3)],[a_(1),1+a_(2),a_(3)],[a_(1),a_(2),1+a_(3)]|=1+a_(1)+a_(2)+a_(3).

If a_(1), a_(2), a_(3), a_(4), a_(5) are consecutive terms of an arithmetic progression with common difference 3, then the value of |(a_(3)^(2),a_(2),a_(1)),(a_(4)^(2),a_(3),a_(2)),(a_(5)^(2),a_(4),a_(3))| is

If a_(1),a_(2),a_(3),a_(4) and a_(5) are in AP with common difference ne 0, find the value of sum_(i=1)^(5)a_(i) " when " a_(3)=2 .

(a_(1))/(a_(1)+a_(2))+(a_(3))/(a_(3)+a_(4))=(2a_(2))/(a_(2)+a_(3))

If terms a_(1),a_(2),a_(3)...,a_(50) are in A.P and a_(6)=2, then the value of common difference at which maximum value of a_(1)a_(4)a_(5) occur is

If a_(1),a_(2)a_(3),….,a_(15) are in A.P and a_(1)+a_(8)+a_(15)=15 , then a_(2)+a_(3)+a_(8)+a_(13)+a_(14) is equal to

Suppose a_(1),a_(2),a_(3) are in A.P. and b_(1),b_(2),b_(3) are in H.P. and let Delta=|(a_(1)-b_(1),a_(1)-b_(2),a_(1)-b_(3)),(a_(2)-b_(1),a_(2)-b_(2),a_(2)-b_(3)),(a_(3)-b_(1),a_(3)-b_(2),a_(3)-b_(3))| then prove that