MathDB
Problems
Contests
National and Regional Contests
India Contests
India LIMIT
2020 LIMIT
2020 LIMIT Category 2
4
Fibonacci mod 3
Fibonacci mod 3
Source: LIMIT 2020 Cat 2 Obj P4
May 25, 2020
limit
Sequence
number theory
Problem Statement
Define the sequence
{
a
n
}
n
≥
1
\{a_n\}_{n\geq 1}
{
a
n
}
n
≥
1
as
a
n
=
n
−
1
a_n=n-1
a
n
=
n
−
1
,
n
≤
2
n\leq 2
n
≤
2
and
a
n
=
a_n=
a
n
=
remainder left by
a
n
−
1
+
a
n
−
2
a_{n-1}+a_{n-2}
a
n
−
1
+
a
n
−
2
when divided by
3
3
3
∀
n
≥
2
\forall n\geq 2
∀
n
≥
2
. Then
∑
i
=
2018
2025
a
i
=
\sum_{i=2018}^{2025}a_i=
∑
i
=
2018
2025
a
i
=
?(A)
6
6
6
(B)
7
7
7
(C)
8
8
8
(D)
9
9
9
Back to Problems
View on AoPS