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1990 Greece Junior Math Olympiad
1
1
Part of
1990 Greece Junior Math Olympiad
Problems
(1)
fibonacci recurrence for juniors - Greece Juniors 1990 p1
Source:
9/14/2024
Considee thr positive integers
a
1
,
a
2
,
.
.
.
,
a
10
a_1,a_2,...,a_{10}
a
1
,
a
2
,
...
,
a
10
such that from the third and on, each it the sum of it's two previous terms (i.e.
a
3
=
a
2
+
a
1
a_3=a_2+a_1
a
3
=
a
2
+
a
1
,
a
4
=
a
3
+
a
2
a_4=a_3+a_2
a
4
=
a
3
+
a
2
, ...). If
a
5
=
7
a_5=7
a
5
=
7
, find
a
10
a_{10}
a
10
.
Fibonacci
algebra