If `a_1, a_2, a_3, a_n` are in H.P. and `f(k)=(sum_(r=1)^n a_r)-a_k ,t h e n` `(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 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 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 in H.P and f(k)=(Sigma_(r=1)^(n) a_r)-a_k then a_1/f(1),a_2/f(3),….,a_n/f(n) are in

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

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 A.P. [1/(a_1a_n)+1/(a_2a_(n-1))+1/(a_3a_(n-2))+..+1/(a_na_1)]

If a_1, a_2, a_3 ….. a_n are in AP, then prove that frac(1)(a_1 a_2)+frac(1)(a_2 a_3)+frac(1)(a_3 a_4)+.....+frac(1)(a_(n-1) a_n)=frac(n-1)(a_1 a_n)

"If "a_1,a_2,a_3,.....,a_n" are in AP, prove that "a_(1)+a_(n)=a_(r)+a_(n-r+1)""

If in a progression a_1, a_2, a_3, e t cdot,(a_r-a_(r+1)) bears a constant atio with a_rxxa_(r+1) , then the terms of the progression are in a. A.P b. G.P. c. H.P. d. none of these

If in a progression a_1, a_2, a_3,.......... e tc dot,(a_r-a_(r+1)) bears a constant ratio with a_rxxa_(r+1) , then the terms of the progression are in a. A.P b. G.P. c. H.P. d. none of these