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Netherlands Contests
Dutch Mathematical Olympiad
1989 Dutch Mathematical Olympiad
1
1
Part of
1989 Dutch Mathematical Olympiad
Problems
(1)
a_n=4a_{n-1}-a_{n-2}
Source: Netherlands - Dutch MO 1989 p1
12/25/2022
For a sequence of integers
a
1
,
a
2
,
a
3
,
.
.
.
a_1,a_2,a_3,...
a
1
,
a
2
,
a
3
,
...
with
0
<
a
1
<
a
2
<
a
3
<
.
.
.
0<a_1<a_2<a_3<...
0
<
a
1
<
a
2
<
a
3
<
...
applies:
a
n
=
4
a
n
−
1
−
a
n
−
2
f
o
r
n
>
2
a_n=4a_{n-1}-a_{n-2} \,\,\, for \,\,\, n > 2
a
n
=
4
a
n
−
1
−
a
n
−
2
f
or
n
>
2
It is further given that
a
4
=
194
a_4 = 194
a
4
=
194
. Calculate
a
5
a_5
a
5
.
algebra
Sequence
recurrence relation