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

Options

A. A.P
B. G.P
C. H.P
D. none of these

Answer

C

Explanation

`a_(1),a_(2),….,a_(n)` are in H.P.
`rArrcdot1/a_(1),1/a_(2),…,1/a_(n)` are in A.P.
`rArr(a_(1)+a_(2)+a_(3)+..+a_(n))/a_(1),(a_(1)+a_(2)+a_(3)+..+a_(n))/a_(2),…,(a_(1)+a_(2)+a_(3)+..+a_(n))/a_(n)` are in A.P.
`=1+(a_(2)+a_(3)+..+a_(n))/a_(1),1+(a_(1)+a_(3)+..+a_(n))/a_(2),....,1+(a_(1)+a_(2)+...+a_(n-1))/a_(n)` are in A.P.
`rArr(a_(2)+a_(3)+...+a_(n))/a_(1),(a_(1)+a_(3)+..+a_(n))/a_(2),...,(a_(1)+a_(2)+...+a_(n-1))/a_(n)` are in A.P.
`rArra_(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 H.P.