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Byju's Answer
Standard XII
Mathematics
Sequence
A sequence is...
Question
A sequence is defined by
a
n
=
n
2
−
1
n
+
1
. The difference of its 1000th and 900th term is
A
100
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B
200
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C
300
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D
1
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Solution
The correct option is
A
100
a
n
=
n
2
−
1
n
+
1
=
(
n
+
1
)
(
n
−
1
)
n
+
1
=
n
−
1
a
1000
−
a
900
=
(
1000
−
1
)
−
(
900
−
1
)
=
100
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0
Similar questions
Q.
A sequence is defined by
a
n
=
n
2
−
1
n
+
1
. The difference of its 1000th and 900th term is
Q.
Write the first five terms sequence defined by
a
n
=
(
−
1
)
n
−
1
.
2
n
Q.
Find the
18
t
h
and
25
t
h
terms of the sequence defined by
a
n
=
⎧
⎪
⎨
⎪
⎩
n
(
n
+
3
)
,
i
f
n
ϵ
N
and n is even
2
n
n
2
+
1
,
i
f
n
ϵ
N
and n is odd.
Q.
Write the first three terms in each of the sequence defined by the following :
(i)
a
n
=
3
n
+
2
(ii)
a
n
=
n
2
+
1
Q.
Show that the sequence, defined by its nth term
3
+
n
4
,
forms an AP. Also, find the common difference of it.
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