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2005 AIME Problems
11
A Sequence of Real Numbers
A Sequence of Real Numbers
Source:
November 13, 2005
induction
Sequences
Problem Statement
Let
m
m
m
be a positive integer, and let
a
0
,
a
1
,
…
,
a
m
a_0, a_1,\ldots,a_m
a
0
,
a
1
,
…
,
a
m
be a sequence of reals such that
a
0
=
37
a_0=37
a
0
=
37
,
a
1
=
72
a_1=72
a
1
=
72
,
a
m
=
0
a_m=0
a
m
=
0
, and
a
k
+
1
=
a
k
−
1
−
3
a
k
a_{k+1}=a_{k-1}-\frac{3}{a_k}
a
k
+
1
=
a
k
−
1
−
a
k
3
for
k
=
1
,
2
,
…
,
m
−
1
k=1,2, \dots, m-1
k
=
1
,
2
,
…
,
m
−
1
. Find
m
m
m
.
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