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Question
Which term of the following sequences :
(a)
2
,
2
2
,
4
,
.
.
.
i
s
1
2
8
?
(b)
3
,
3
,
3
3
,
.
.
.
is
7
2
9
?
(c)
3
1
,
9
1
,
2
7
1
,
.
.
.
is
1
9
6
8
3
1
?
Easy
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Solution
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(a) The given sequence is,
2
,
2
2
,
4
,
.
.
.
Clearly given sequence is in G.P
With
a
=
2
and
r
=
2
2
2
=
2
Let the
n
t
h
term of the given sequence be
1
2
8
.
a
n
=
a
r
n
−
1
⇒
(
2
)
(
2
)
n
−
1
=
1
2
8
⇒
(
2
)
(
2
)
2
n
−
1
=
(
2
)
7
⇒
(
2
)
2
n
−
1
+
1
=
(
2
)
7
⇒
2
n
−
1
=
6
⇒
n
−
1
=
1
2
⇒
n
=
1
3
Thus, the
1
3
t
h
term of the given sequence is
1
2
8
.
(b) The given sequence is
3
,
3
,
3
3
Clearly this sequence is in G.P
with,
a
=
3
and
r
=
3
3
=
3
Let the
n
t
h
term of the given sequence be
7
2
9
.
a
n
=
a
r
n
−
1
⇒
a
r
n
−
1
=
7
2
9
⇒
(
3
)
(
3
)
n
−
1
=
7
2
9
⇒
(
3
)
2
1
(
3
)
2
n
−
1
=
(
3
)
6
∴
2
1
+
2
n
−
1
=
6
⇒
2
1
+
n
−
1
=
6
⇒
n
=
1
2
Thus, the
1
2
t
h
term of the given sequence is
7
2
9
.
(c) The given sequence is,
3
1
,
9
1
,
2
7
1
,
.
.
.
Clearly this sequence is in G.P
With
a
=
3
1
and
r
=
9
1
÷
3
1
=
3
1
Let the
n
t
h
term of the given sequence be
1
9
6
8
3
1
a
n
=
a
r
n
−
1
⇒
a
r
n
−
1
=
1
9
6
8
3
1
⇒
(
3
1
)
(
3
1
)
n
−
1
=
1
9
6
8
3
1
⇒
(
3
1
)
n
=
(
3
1
)
9
⇒
n
=
9
Thus, the
9
t
h
term of the given sequence is
1
9
6
8
3
1
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Mathematics
NCERT
Exercise 9.3
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