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If a1,a2,a3…an are in H.P and f(k)=(Sigm...

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

A

A.P

B

G.P

C

H.P

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
`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.
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