If `a_1,a_2,a_3..........,a_n` is a GP of nonzero non-negative numers, then `loga_1,loga_2,loga_3,............,loga_n` is an AP and vice versa.

(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,..........., a_n be an A.P. of non-zero terms, prove that : 1/(a_1 a_2)+1/(a_2 a_3)+ ............. + 1/(a_(n-1) a_n)= (n-1)/(a_1 a_n) .

2(loga+loga^2+loga^3+loga^4+................+loga^n) is equal to

If a_1,a_2,a_3,.....a_n.... are in G.P. then the determinant Delta=|[loga_n,loga_(n+1),loga_(n+2)],[loga_(n+3),loga_(n+4),loga_(n+5)],[loga_(n+6),loga_(n+7),loga_(n+8)]| is equal to-

If a_1,a_2,a_3,.....a_n.... are in G.P. then the determinant 'Delta=|[loga_n , loga_(n+1),loga_(n+2)],[loga_(n+3),loga_(n+4),loga_(n+5)],[loga_(n+6),loga_(n+7),loga_(n+8)]| is equal to- (A) -2 (B) 1 (C) -1 (D) 0

If a_1,a_2,a_3,.....a_n.... are in G.P. then the determinant Delta=|[loga_n,loga_(n+1),loga_(n+2)],[loga_(n+3),loga_(n+4),loga_(n+5)],[loga_(n+6),loga_(n+7),loga_(n+8)]| is equal to- (A) -2 (B) 1 (C) -1 (D) 0

If a_1,a_2,a_3,.....a_n.... are in G.P. then the determinant Delta=|[log a_n, log a_(n+1), log a_(n+2)],[log a_(n+3),loga_(n+4),log a_(n+5)],[log a_(n+6),log a_(n+7),log a_(n+8)]| is equal to- (A) -2 (B) 1 (C) -1 (D) 0

We know that, if a_1, a_2, ..., a_n are in H.P. then 1/a_1,1/a_2,.....,1/a_n are in A.P. and vice versa. If a_1, a_2, ..., a_n are in A.P. with common difference d, then for any b (>0), the numbers b^(a_1),b^(a_2),b^9a_3),........,b^(a_n) are in G.P. with common ratio b^d. If a_1, a_2, ..., a_n are positive and in G.P. with common ration, then for any base b (b> 0), log_b a_1 , log_b a_2,...., log_b a_n are in A.P. with common difference logor.If x, y, z are respectively the pth, qth and the rth terms of an A.P., as well as of a G.P., then x^(z-x),z^(x-y) is equal to

If a_1,a_2,a_3...a_n are in HP and f(k)=sum_(r=1)^na_r-a_k, then a_1/(f(1)),a_2/(f(2)),a_3/(f(3)),......a_n/(f(n)) are in

If a_1,a_2,a_3,....a_n are positive real numbers whose product is a fixed number c, then the minimum value of a_1+a_2+.......a_(n-1)+2a_n is