MathDB
Problems
Contests
National and Regional Contests
Turkey Contests
National Olympiad First Round
2006 National Olympiad First Round
3
Turkey NMO 2006 1st Round - P03 (Algebra)
Turkey NMO 2006 1st Round - P03 (Algebra)
Source:
February 2, 2013
Problem Statement
a
1
=
−
1
a_1=-1
a
1
=
−
1
,
a
2
=
2
a_2=2
a
2
=
2
, and
a
n
=
a
n
−
1
a
n
−
2
a_n=\frac {a_{n-1}}{a_{n-2}}
a
n
=
a
n
−
2
a
n
−
1
for
n
≥
3
n\geq 3
n
≥
3
. What is
a
2006
a_{2006}
a
2006
?
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
a
n
>
−
2
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
a
n
>
−
1
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
a
n
>
−
1
2
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
a
n
>
1
2
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
a
n
>
2
<span class='latex-bold'>(A)</span>\ -2 \qquad<span class='latex-bold'>(B)</span>\ -1 \qquad<span class='latex-bold'>(C)</span>\ -\frac 12 \qquad<span class='latex-bold'>(D)</span>\ \frac 12 \qquad<span class='latex-bold'>(E)</span>\ 2
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
an
>
−
2
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
an
>
−
1
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
an
>
−
2
1
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
2
1
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
2
Back to Problems
View on AoPS