Question

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

Answer 1

Correct Answer - C
`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.