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2009 AMC 10A Problem 15

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2009 AMC 10A Problem 15AMC 10 Step by Step

Name: Date: September 13, 2026

Sequences & Series · difficulty 3 of 5 · about 4 min · position P11-15

The figures $F_1$ , $F_2$ , $F_3$ , and $F_4$ shown are the first in a sequence of figures. For $n\ge3$ , $F_n$ is constructed from $F_{n - 1}$ by surrounding it with a square and placing one more diamond on each side of the new square than $F_{n - 1}$ had on each side of its outside square. For example, figure $F_3$ has $13$ diamonds. How many diamonds are there in figure $F_{20}$ ?

A)
$401$
B)
$485$
C)
$585$
D)
$626$
E)
$761$

2009 AMC 10A Problem 15

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