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

Options

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

Answer

C

Explanation

`f(k)+a_(k)=sum_(r=1)^(n)a_(r)=lamda` (say)
`therefore f(k)=lamda-a_(k)`
`rArr(f(k))/a_(k)=lamda/(a_(k))-1`
`therefore(f(1))/a_(1),(f(2))/a_(2),…,(f(n))/a_(n)` are in A.P.
So `a_(1)/(f(1)),a_(2)/(f(2)),….,a_(n)/(f(n))` are in H.P.