If `a_(1),a_(2),a_(3),....` are in G.P. with common ratio as `r^(2)` then `log a_(1),log a_(2),log a_(3),....` will be in

If a_(1),a_(2),a_(3)… are in G.P. then the value of |{:(log a_(n),loga_(n+1),log a_(n+2)),(log a_(n+3),log a_(n+4),log a_(n+5)),(log a_(n+6),log a_(n+7),log a_(n+8)):}| is

(vii) If a_(1);a_(2);a_(3)............a_(n) is a GP of nonzero non-negative,then log a_(1);log a_(2);log a_(3).........log a_(n)...... is an AP and vice versa.

If a_(1),a_(2),a_(3),...... are in G.P.then the value of determinant det[[log(a_(n)),log(a_(n+1)),log(a_(n+2))log(a_(n+3)),log(a_(n+4)),log(a_(n+5))log(a_(n+6)),log(a_(n+7)),log(a_(n+8))]] equals

If a_(1), a_(2), a_(3)(a_(1)gt 0) are in G.P. with common ratio r, then the value of r, for which the inequality 9a_(1)+5 a_(3)gt 14 a_(2) holds, can not lie in the interval

If a_(1),a_(2),a_(3)"....." are in GP with first term a and common rario r, then (a_(1)a_(2))/(a_(1)^(2)-a_(2)^(2))+(a_(2)a_(3))/(a_(2)^(2)-a_(3)^(2))+(a_(3)a_(4))/(a_(3)^(2)-a_(4)^(2))+"....."+(a_(n-1)a_(n))/(a_(n-1)^(2)-a_(n)^(2)) is equal to

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