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2014 BMT Spring
9
BMT 2014 Spring - Individual 9
BMT 2014 Spring - Individual 9
Source:
January 22, 2022
algebra
Problem Statement
Suppose
a
1
,
a
2
,
.
.
.
a_1, a_2, ...
a
1
,
a
2
,
...
and
b
1
,
b
2
,
.
.
.
b_1, b_2,...
b
1
,
b
2
,
...
are sequences satisfying
a
n
+
b
n
=
7
a_n + b_n = 7
a
n
+
b
n
=
7
,
a
n
=
2
b
n
−
1
−
a
n
−
1
a_n = 2b_{n-1} - a_{n-1}
a
n
=
2
b
n
−
1
−
a
n
−
1
, and
b
n
=
2
a
n
−
1
−
b
n
−
1
b_n = 2a_{n-1} - b_{n-1}
b
n
=
2
a
n
−
1
−
b
n
−
1
, for all
n
n
n
. If
a
1
=
2
a_1 = 2
a
1
=
2
, find
(
a
2014
)
2
−
(
b
2014
)
2
(a_{2014})^2 - (b_{2014})^2
(
a
2014
)
2
−
(
b
2014
)
2
. .
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