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All-Russian Olympiad
1962 All-Soviet Union Olympiad
3
Sequence of Integers
Sequence of Integers
Source: 1962 All-Soviet Union Olympiad
January 15, 2018
Russia
algebra
Sequences
Problem Statement
Given integers
a
0
,
a
1
,
.
.
.
,
a
100
a_0,a_1, ... , a_{100}
a
0
,
a
1
,
...
,
a
100
, satisfying
a
1
>
a
0
a_1>a_0
a
1
>
a
0
,
a
1
>
0
a_1>0
a
1
>
0
, and
a
r
+
2
=
3
a
r
+
1
−
2
a
r
a_{r+2}=3 a_{r+1}-2a_r
a
r
+
2
=
3
a
r
+
1
−
2
a
r
for
r
=
0
,
1
,
.
.
.
,
98
r=0, 1, ... , 98
r
=
0
,
1
,
...
,
98
. Prove
a
100
>
299
a_{100}>299
a
100
>
299
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