Question 41 - Week 7 Practice | Prasnya
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Week 7
Question 41
00:00
Est. 2 min
Marks:
+2.00
0.00
Consider a sequence
(
1
,
2
,
3
,
4
,
5
,
6
,
…
)
(1,2,3,4,5,6,\ldots)
, that is,
a
n
=
n
a_n=n
for all
n
∈
N
n\in\mathbb{N}
. Which of the following sequences are subsequences of
{
a
n
}
\{a_n\}
?
Multiple correct
EASY Difficulty
20 November 2022
A
(
1
,
3
,
1
,
3
,
…
)
(1,3,1,3,\ldots)
, that is,
b
n
=
1
b_n=1
if
n
n
is odd and
b
n
=
3
b_n=3
if
n
n
is even.
B
(
1
,
3
,
5
,
7
,
…
)
(1,3,5,7,\ldots)
, that is,
b
n
=
2
n
−
1
b_n=2n-1
for all
n
∈
N
n\in\mathbb{N}
.
C
(
1
,
1
,
2
,
2
,
3
,
3
,
…
)
(1,1,2,2,3,3,\ldots)
, that is,
b
n
=
n
+
1
2
b_n=\frac{n+1}{2}
if
n
n
is odd and
b
n
=
n
2
b_n=\frac{n}{2}
if
n
n
is even.
D
(
1
,
8
,
27
,
64
,
…
)
(1,8,27,64,\ldots)
, that is,
b
n
=
n
3
b_n=n^3
for all
n
∈
N
n\in\mathbb{N}
.
