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2
Similar Geometric Sequences
Similar Geometric Sequences
Source: 2012 AIME II Problem 2
March 29, 2012
ratio
AMC
Problem Statement
Two geometric sequences
a
1
,
a
2
,
a
3
,
…
a_1,a_2,a_3,\ldots
a
1
,
a
2
,
a
3
,
…
and
b
1
,
b
2
,
b
3
…
b_1,b_2,b_3\ldots
b
1
,
b
2
,
b
3
…
have the same common ratio, with
a
1
=
27
a_1=27
a
1
=
27
,
b
1
=
99
b_1=99
b
1
=
99
, and
a
15
=
b
11
a_{15}=b_{11}
a
15
=
b
11
. Find
a
9
.
a_9.
a
9
.
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