`3, -3^(2), 3^(3), ……….a_(6) = …………..`

If a_(1), a_(2), a_(3), ……. , a_(n) are in A.P. 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

If a_(1), a_(2), a_(3), a_(4), a_(5) and a_(6) are six arithmetic means between 3 and 31, then a_(6) - a_(5) and a_(1) + a_(6) are respectively =

If ( a_(2)a_(3))/( a_(1) a_(4)) = ( a_(2) + a_(3))/( a_(1) + a_(4) ) = 3 ((a_(2) - a_(3))/(a_(1) - a_(4))) , then : a_(1) , a_(2) , a_(3) , a_(4) are in :

The value of the determinant Delta = |((1 - a_(1)^(3) b_(1)^(3))/(1 - a_(1) b_(1)),(1 - a_(1)^(3) b_(2)^(3))/(1 - a_(1) b_(2)),(1 - a_(1)^(3) b_(3)^(3))/(1 - a_(1) b_(3))),((1 - a_(2)^(3) b_(1)^(3))/(1 - a_(2) b_(1)),(1 - a_(2)^(3) b_(2)^(3))/(1 - a_(2) b_(2)),(1 - a_(2)^(3) b_(3)^(3))/(1 - a_(2) b_(3))),((1 - a_(3)^(3) b_(1)^(3))/(1 - a_(3) b_(1)),(1 - a_(3)^(3) b_(2)^(3))/(1 - a_(3) b_(2)),(1 - a_(3)^(3) b_(3)^(3))/(1 - a_(3) b_(3)))| , is

For the A.P., a_(1),a_(2),a_(3) ,…………… if (a_(4))/(a_(7))=2/3 , find (a_(6))/(a_(8))