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2023 UMD Math Competition Part I
#22
Sequence
Sequence
Source: UMD 2023 I #22
October 22, 2023
algebra
UMD
Problem Statement
A sequence
a
1
,
a
2
,
…
a_1, a_2, \ldots
a
1
,
a
2
,
…
satisfies
a
1
=
5
2
a_1 = \dfrac 52
a
1
=
2
5
and
a
n
+
1
=
a
n
2
−
2
a_{n + 1} = {a_n}^2 - 2
a
n
+
1
=
a
n
2
−
2
for all
n
≥
1.
n \ge 1.
n
≥
1.
Let
M
M
M
be the integer which is closest to
a
2023
.
a_{2023}.
a
2023
.
The last digit of
M
M
M
equals
a
.
0
b
.
2
c
.
4
d
.
6
e
.
8
\mathrm a. ~ 0\qquad \mathrm b.~2\qquad \mathrm c. ~4 \qquad \mathrm d. ~6 \qquad \mathrm e. ~8
a
.
0
b
.
2
c
.
4
d
.
6
e
.
8
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