MathDB
Problems
Contests
National and Regional Contests
USA Contests
USA - Other Middle and High School Contests
Math Prize For Girls Problems
2011 Math Prize For Girls Problems
11
11
Part of
2011 Math Prize For Girls Problems
Problems
(1)
Math Prize 2011 Problem 11
Source:
9/19/2011
The sequence
a
0
a_0
a
0
,
a
1
a_1
a
1
,
a
2
a_2
a
2
,
…
\ldots\,
…
satisfies the recurrence equation
a
n
=
2
a
n
−
1
−
2
a
n
−
2
+
a
n
−
3
a_n = 2 a_{n-1} - 2 a_{n - 2} + a_{n - 3}
a
n
=
2
a
n
−
1
−
2
a
n
−
2
+
a
n
−
3
for every integer
n
≥
3
n \ge 3
n
≥
3
. If
a
20
=
1
a_{20} = 1
a
20
=
1
,
a
25
=
10
a_{25} = 10
a
25
=
10
, and
a
30
=
100
a_{30} = 100
a
30
=
100
, what is the value of
a
1331
a_{1331}
a
1331
?
linear algebra
matrix
algebra
polynomial
trigonometry