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Mathematics
Problem
Let
⟨
a
n
⟩
\langle a_n \rangle
⟨
a
n
⟩
be a sequence such that
a
0
=
0
a_0 = 0
a
0
=
0
,
a
1
=
1
2
a_1 = \frac{1}{2}
a
1
=
2
1
and
2
a
n
+
2
=
5
a
n
+
1
−
3
a
n
2a_{n+2} = 5a_{n+1} - 3a_n
2
a
n
+
2
=
5
a
n
+
1
−
3
a
n
,
n
=
0
,
1
,
2
,
3
,
…
n = 0, 1, 2, 3, \dots
n
=
0
,
1
,
2
,
3
,
…
. Then
∑
k
=
1
100
a
k
\sum_{k=1}^{100} a_k
∑
k
=
1
100
a
k
is equal to: (a)
3
a
99
−
100
3a_{99} - 100
3
a
99
−
100
(b)
3
a
100
−
100
3a_{100} - 100
3
a
100
−
100
(c)
3
a
100
+
100
3a_{100} + 100
3
a
100
+
100
(d)
3
a
99
+
100
3a_{99} + 100
3
a
99
+
100
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