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Problems
Contests
National and Regional Contests
Turkey Contests
National Olympiad First Round
2008 National Olympiad First Round
11
11
Part of
2008 National Olympiad First Round
Problems
(1)
Turkey NMO 2008 1st Round - P11 (Algebra)
Source:
8/25/2012
Sequence
(
a
n
)
(a_n)
(
a
n
)
is defined as
a
n
+
1
−
2
a
n
+
a
n
−
1
=
7
a_{n+1}-2a_n+a_{n-1}=7
a
n
+
1
−
2
a
n
+
a
n
−
1
=
7
for every
n
≥
2
n\geq 2
n
≥
2
, where
a
1
=
1
,
a
2
=
5
a_1 = 1, a_2=5
a
1
=
1
,
a
2
=
5
. What is
a
17
a_{17}
a
17
?
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
a
n
>
895
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
a
n
>
900
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
a
n
>
905
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
a
n
>
910
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
a
n
>
None of the above
<span class='latex-bold'>(A)</span>\ 895 \qquad<span class='latex-bold'>(B)</span>\ 900 \qquad<span class='latex-bold'>(C)</span>\ 905 \qquad<span class='latex-bold'>(D)</span>\ 910 \qquad<span class='latex-bold'>(E)</span>\ \text{None of the above}
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
an
>
895
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
an
>
900
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
an
>
905
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
910
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
None of the above