If `a_1, a_2, ,a_n` are in H.P., then `(a_1)/(a_2+a_3++a_n),(a_2)/(a_1+a_3++a_n), ,(a_n)/(a_1+a_2++a_(n-1))` are in a. A.P b. G.P. c. H.P. d. none of these

If a_1,a_2,a_3,.....,a_n are in AP, prove that 1/(a_1a_2)+1/(a_2a_3)+1/(a_3a_4)+...+1/(a_(n-1)a_n)=(n-1)/(a_1a_n) .

If a_1,a_2,a_3……..a_n are in H.P. and f(k) = sum_(r=1)^na_r-a_k then (f(1))/a_1, (f(2))/a_3 ….f(n)/a_n are (A) A.P. (B) G.P. (C) H.P. (D) none of these

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………. are in H.P. and f(k) =sum_(r=1)^n a_r-a_k, the a_1/(f(1)), a_2/(f(2)), a_3/(f(3)), …….., a_n/(f(n)) are in (A) A.P. (B) G.P (C) H.P. (D) none of these

If x,a_1,a_2,a_3,…..a_n epsilon R and (x-a_1+a_2)^2+(x-a_2+a_3)^2+…….+(x-a_(n-1)+a_n)^2le0 , then a_1,a_2,a_3………a_n are in (A) AP (B) GP (C) HP (D) none of these

If a_1,a_2,a_3….a_(2n+1) are in A.P then (a_(2n+1)-a_1)/(a_(2n+1)+a_1)+(a_2n-a_2)/(a_(2n)+a_2)+....+(a_(n+2)-a_n)/(a_(n+2)+a_n) is equal to

Let a_1,a_2,a_3 …. a_n be in A.P. If 1/(a_1a_n)+1/(a_2a_(n-1)) +… + 1/(a_n a_1) = k/(a_1 + a_n) (1/a_1 + 1/a_2 + …. 1/a_n) , then k is equal to :