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Purple Comet Problems
2005 Purple Comet Problems
17
Problem 17, Spring 2005 , HS
Problem 17, Spring 2005 , HS
Source:
June 23, 2011
function
Problem Statement
Functions
f
f
f
and
g
g
g
are defined so that
f
(
1
)
=
4
f(1) = 4
f
(
1
)
=
4
,
g
(
1
)
=
9
g(1) = 9
g
(
1
)
=
9
, and for each integer
n
≥
1
n \ge 1
n
≥
1
,
f
(
n
+
1
)
=
2
f
(
n
)
+
3
g
(
n
)
+
2
n
f(n+1) = 2f(n) + 3g(n) + 2n
f
(
n
+
1
)
=
2
f
(
n
)
+
3
g
(
n
)
+
2
n
and
g
(
n
+
1
)
=
2
g
(
n
)
+
3
f
(
n
)
+
5
g(n+1) = 2g(n) + 3 f(n) + 5
g
(
n
+
1
)
=
2
g
(
n
)
+
3
f
(
n
)
+
5
. Find
f
(
2005
)
−
g
(
2005
)
f(2005) - g(2005)
f
(
2005
)
−
g
(
2005
)
.
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