Insert 4 hm between 1 and 1 divide 16
Answers
Answer:
we have to insert 4 elements of the sequence between1/2 and 1/22
Let ,
H
1
,
H
2
,
H
3
,
H
4
be the 4 harmonic means between
1
2
and
1
22
⇒
1
2
,
H
1
,
H
2
,
H
3
,
H
4
,
1
22
are in H.P.
⇒
2
,
1
H
1
,
1
H
2
,
1
H
3
,
1
H
4
,
22
are in A.P.
∴
a
1
=
2
,
a
2
=
1
H
1
,
a
3
=
1
H
2
,
a
4
=
1
H
3
,
a
5
=
1
H
4
,
a
6
=
22
Let ,
d
=
common difference of arithmetic sequence.
Now,
a
6
=
a
1
+
(
6
−
1
)
d
=
22
⇒
2
+
5
d
=
22
⇒
5
d
=
22
−
2
=
20
⇒
d
=
4
So ,
a
2
=
2
+
4
=
6
⇒
1
H
1
=
6
⇒
H
1
=
1
6
a
3
=
6
+
4
=
10
⇒
1
H
2
=
10
⇒
H
2
=
1
10
a
4
=
10
+
4
=
14
⇒
1
H
3
=
14
⇒
H
3
=
1
14
a
5
=
14
+
4
=
18
⇒
1
H
4
=
18
⇒
H
4
=
1
18
Hence ,
→
1
6
,
1
10
,
1
14
,
1
18
are four Harmonic means between
1
2
and
1
22
..............................................................................................................................
Hope this will help you