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

If `a_1, a_2, a_3, a_n` are in H.P. and `f(k)=(sum_(r=1)^n a_r)-a_k ,t h e n` `(a_1)/(f(1)),(a_2)/(f(2)),(a_3)/(f(3)), ,(a_n)/(f(n)),` are in a. A.P b. G.P. c. H.P. d. none of these

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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