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Byju's Answer
Standard XI
Mathematics
Harmonic Mean
Insert two ha...
Question
Insert two harmonic means between
5
and
11
.
Open in App
Solution
Insert two
H
M
between
5
and
11
∴
a
=
5
and
b
=
11
Let
H
1
and
H
2
be the two
H
M
∴
1
5
,
1
H
1
,
1
H
2
,
1
11
are in
A
.
P
.
Let
d
is the common difference of this in
A
.
P
∴
1
11
=
(
n
+
2
)
t
h
term
=
T
n
+
2
⟹
1
11
=
1
5
+
(
(
n
+
2
)
−
1
)
d
d
=
1
11
−
1
5
(
n
+
1
)
∴
For
n
=
2
d
=
(
1
11
−
1
5
)
3
=
5
−
11
55
×
3
=
−
6
3
×
55
=
−
2
55
∴
T
2
=
1
5
+
(
2
−
1
)
×
−
2
55
=
11
−
2
55
=
9
55
=
1
H
1
T
3
=
1
5
+
(
2
×
−
2
55
)
=
7
55
=
1
H
2
∴
H
1
=
55
9
H
2
=
55
7
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