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4
x_n=[(n+1)a]-[na], a=\sqrt{2013/2014} (HOMC 2013 Q4)
x_n=[(n+1)a]-[na], a=\sqrt{2013/2014} (HOMC 2013 Q4)
Source:
July 30, 2019
Sequence
algebra
floor function
Problem Statement
Let
x
0
=
[
a
]
,
x
1
=
[
2
a
]
−
[
a
]
,
x
2
=
[
3
a
]
−
[
2
a
]
,
x
3
=
[
3
a
]
−
[
4
a
]
,
x
4
=
[
5
a
]
−
[
4
a
]
,
x
5
=
[
6
a
]
−
[
5
a
]
,
.
.
.
,
x_0 = [a], x_1 = [2a] - [a], x_2 = [3a] - [2a], x_3 = [3a] - [4a],x_4 = [5a] - [4a],x_5 = [6a] - [5a], . . . ,
x
0
=
[
a
]
,
x
1
=
[
2
a
]
−
[
a
]
,
x
2
=
[
3
a
]
−
[
2
a
]
,
x
3
=
[
3
a
]
−
[
4
a
]
,
x
4
=
[
5
a
]
−
[
4
a
]
,
x
5
=
[
6
a
]
−
[
5
a
]
,
...
,
where
a
=
2013
2014
a=\frac{\sqrt{2013}}{\sqrt{2014}}
a
=
2014
2013
.The value of
x
9
x_9
x
9
is: (A):
2
2
2
(B):
3
3
3
(C):
4
4
4
(D):
5
5
5
(E): None of the above.
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