Insert three harmonic means between 1/3 and 1/9
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Insert two harmonic means between 5 and 11.
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ANSWER
Insert two HM between 5 and 11
∴a=5 and b=11
Let H
1
and H
2
be the two HM
∴
5
1
,
H
1
1
,
H
2
1
,
11
1
are in A.P.
Let d is the common difference of this in A.P
∴
11
1
=(n+2)
th
term =T
n+2
⟹
11
1
=
5
1
+((n+2)−1)d
d=
(n+1)
11
1
−
5
1
∴ For n=2
d=
3
(
11
1
−
5
1
)
=
55×3
5−11
=
3×55
−6
=
55
−2
∴T
2
=
5
1
+(2−1)×
55
−2
=
55
11−2
=
55
9
=
H
1
1
T
3
=
5
1
+(2×
55
−2
)=
55
7
=
H
2
1
∴H
1
=
9
55
H
2
=
7
55
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