If `a_(1),a_(2),a_(3),a_(4),a_(5),a_(6)` are in A.P , then prove that the system of equations `a_(1)x+a_(2)y=a_(3),a_(4)x+a_(5)y = a_(6)` is consistent .

If a_(1), a_(2), a_(3), …., a_(9) are in GP, then what is the value of the following determinant? |(ln a_(1), ln a_(2), ln a_(3)),(lna_(4), lna_(5), ln a_(6)), (ln a_(7), ln a_(8), ln a_(9))|

Let S be the set of 6 -digit numbers a_(1)a_(2)a_(3)a_(4)a_(5)a_(6) (all digits distinct) where a_(1)>a_(2)>a_(3)>a_(4)

If a_(1)+a_(2)+a_(3)+a_(4)+a_(5)...+a_(n) for all a_(i)>0,i=1,2,3dots n. Then the maximum value of a_(1)^(2)a_(2)a_(3)a_(4)a_(5)..a_(n) is

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)

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 .

Let (a_(1),a_(2),a_(3),a_(4),a_(5)) denote a re=arrangement of (3,-5,7,4-9), then a_(1)x^(4)+a_(2)x^(3)+a_(3)x^(2)+a_(4)+a_(5)=0 has

It a_(1) , a_(2) , a_(3) a_(4) be in G.P. then prove that (a_(2)-a_(3))^(2) + (a_(3) - a_(1))^(2) + (a_(4) +a_(2))^(2) = (a_(1)-a_(4))^(2)

If a_(1),a_(2),a_(3),a_(4),a_(5) are positive real numbers in A.P. and a_(1),a_(2).a_(4).a_(5)=16, then the minimum value of a_(3) is equal to