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Question

Insert two harmonic means between 5 and 11.

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Solution

Insert two HM between 5 and 11
a=5 and b=11
Let H1 and H2 be the two HM
15,1H1,1H2,111 are in A.P.
Let d is the common difference of this in A.P
111=(n+2)th term =Tn+2

111=15+((n+2)1)d

d=11115(n+1)

For n=2
d=(11115)3=51155×3=63×55=255

T2=15+(21)×255=11255=955=1H1

T3=15+(2×255)=755=1H2

H1=559H2=557


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