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8
2017 Algebra #8
2017 Algebra #8
Source:
August 20, 2022
2017
Algebra Test
Problem Statement
Consider the sequence of real numbers
a
n
a_n
a
n
satisfying the recurrence
a
n
a
n
+
2
−
a
n
+
1
2
−
(
n
+
1
)
a
n
a
n
+
1
=
0.
a_na_{n+2}-a_{n+1}^2-(n+1)a_na_{n+1}=0.
a
n
a
n
+
2
−
a
n
+
1
2
−
(
n
+
1
)
a
n
a
n
+
1
=
0.
Given that
a
1
=
1
a_1=1
a
1
=
1
and
a
2
=
2018
a_2=2018
a
2
=
2018
, compute
a
2018
⋅
a
2016
a
2017
2
.
\frac{a_{2018}\cdot a_{2016}}{a_{2017}^2}.
a
2017
2
a
2018
⋅
a
2016
.
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