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If a(a), a (2), a (3),…., a(n) are in H....

If `a_(a), a _(2), a _(3),…., a_(n)` are in H.P. and `f (k)=sum _(r =1) ^(n) a_(r)-a_(k) ` then `(a_(1))/(f(1)), (a_(2))/(f (2)), (a_(3))/(f (n))` are in :

A

A.P.

B

G.P.

C

H.P.

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
It is given that
`a_(1),a_(2),a_(3), . . . ,a_(n)` are in H.P.
`rArr" "(1)/(a_(1)),(1)/(a_(2)),(1)/(a_(3)), . . . ,(1)/(a_(n))` are in A.P.
`rArr" "(underset(r=1)overset(n)suma_(r))/(a_(1)),(underset(r=1)overset(n)suma_(r))/(a_(2)),(underset(r=1)overset(n)suma_(r))/(a_(3)), . . . .,(underset(r=1)overset(n)suma_(r))/(a_(n))` are in A.P.
`rArr" "(f(1)+a_(1))/(a_(1)),(f(2)+a_(2))/(a_(2)),(f(3)+a_(3))/(a_(3)), . . . .,(f(n)+a_(n))/(a_(n))` are in A.P.
`rArr" "(f(1))/(a_(1))+1,(f(2))/(a_(2))+1,(f(3))/(a_(3))+1, . . . ,(f(n))/(a_(n))+1` are in A.P.
`rArr" "(f(1))/(a_(1)),(f(2))/(a_(2)),(f(3))/(a_(3)), . . . .,(f(n))/(a_(n))` are in A.P.
`rArr" "(a_(1))/(f(1)),(a_(2))/(f(2)),(a_(3))/(f(3)), . . .,(a_(n))/(f(n))` are in H.P.
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