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Question 41 - Week 7 Practice | Prasnya
Q41
00:00
20 Nov 2022
Q41.
Consider a sequence
(
1
,
2
,
3
,
4
,
5
,
6
,
…
)
(1,2,3,4,5,6,\ldots)
(
1
,
2
,
3
,
4
,
5
,
6
,
…
)
, that is,
a
n
=
n
a_n=n
a
n
=
n
for all
n
∈
N
n\in\mathbb{N}
n
∈
N
. Which of the following sequences are subsequences of
{
a
n
}
\{a_n\}
{
a
n
}
?
A
(
1
,
3
,
1
,
3
,
…
)
(1,3,1,3,\ldots)
(
1
,
3
,
1
,
3
,
…
)
, that is,
b
n
=
1
b_n=1
b
n
=
1
if
n
n
n
is odd and
b
n
=
3
b_n=3
b
n
=
3
if
n
n
n
is even.
B
(
1
,
3
,
5
,
7
,
…
)
(1,3,5,7,\ldots)
(
1
,
3
,
5
,
7
,
…
)
, that is,
b
n
=
2
n
−
1
b_n=2n-1
b
n
=
2
n
−
1
for all
n
∈
N
n\in\mathbb{N}
n
∈
N
.
C
(
1
,
1
,
2
,
2
,
3
,
3
,
…
)
(1,1,2,2,3,3,\ldots)
(
1
,
1
,
2
,
2
,
3
,
3
,
…
)
, that is,
b
n
=
n
+
1
2
b_n=\frac{n+1}{2}
b
n
=
2
n
+
1
if
n
n
n
is odd and
b
n
=
n
2
b_n=\frac{n}{2}
b
n
=
2
n
if
n
n
n
is even.
D
(
1
,
8
,
27
,
64
,
…
)
(1,8,27,64,\ldots)
(
1
,
8
,
27
,
64
,
…
)
, that is,
b
n
=
n
3
b_n=n^3
b
n
=
n
3
for all
n
∈
N
n\in\mathbb{N}
n
∈
N
.
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Check
Details
Q41
00:00
20 Nov 2022
Q41.
Consider a sequence
(
1
,
2
,
3
,
4
,
5
,
6
,
…
)
(1,2,3,4,5,6,\ldots)
(
1
,
2
,
3
,
4
,
5
,
6
,
…
)
, that is,
a
n
=
n
a_n=n
a
n
=
n
for all
n
∈
N
n\in\mathbb{N}
n
∈
N
. Which of the following sequences are subsequences of
{
a
n
}
\{a_n\}
{
a
n
}
?
A
(
1
,
3
,
1
,
3
,
…
)
(1,3,1,3,\ldots)
(
1
,
3
,
1
,
3
,
…
)
, that is,
b
n
=
1
b_n=1
b
n
=
1
if
n
n
n
is odd and
b
n
=
3
b_n=3
b
n
=
3
if
n
n
n
is even.
B
(
1
,
3
,
5
,
7
,
…
)
(1,3,5,7,\ldots)
(
1
,
3
,
5
,
7
,
…
)
, that is,
b
n
=
2
n
−
1
b_n=2n-1
b
n
=
2
n
−
1
for all
n
∈
N
n\in\mathbb{N}
n
∈
N
.
C
(
1
,
1
,
2
,
2
,
3
,
3
,
…
)
(1,1,2,2,3,3,\ldots)
(
1
,
1
,
2
,
2
,
3
,
3
,
…
)
, that is,
b
n
=
n
+
1
2
b_n=\frac{n+1}{2}
b
n
=
2
n
+
1
if
n
n
n
is odd and
b
n
=
n
2
b_n=\frac{n}{2}
b
n
=
2
n
if
n
n
n
is even.
D
(
1
,
8
,
27
,
64
,
…
)
(1,8,27,64,\ldots)
(
1
,
8
,
27
,
64
,
…
)
, that is,
b
n
=
n
3
b_n=n^3
b
n
=
n
3
for all
n
∈
N
n\in\mathbb{N}
n
∈
N
.
Save
Check
Details
