AMC8 2002

AMC8 2002 · Q11

AMC8 2002 · Q11. It mainly tests Vieta / quadratic relationships (basic), Arithmetic sequences basics.

A sequence of squares is made of identical square tiles. The edge of each square is one tile length longer than the edge of the previous square. The first three squares are shown. How many more tiles does the seventh square require than the sixth?

一个由相同正方形瓦片构成的正方形序列。每个正方形的边长比前一个正方形的边长多一个瓦片长度。展示了前三个正方形。第七个正方形比第六个正方形多需要多少瓦片？

(A) 11 11

(B) 12 12

(D) 14 14

(E) 15 15

Answer

Correct choice: (C)

正确答案：（C）

Solution

(C) To build the second square from the first, add 3 tiles. To build the third from the second, add 5 tiles. The pattern of adding an odd number of tiles continues. For the fourth square, add 7; for the fifth, add 9; for the sixth, add 11 and for the seventh, add 13.

（C）要从第一个正方形建成第二个，需要加 3 块瓷砖。要从第二个建成第三个，需要加 5 块瓷砖。继续遵循每次增加奇数块瓷砖的规律。第四个正方形加 7 块；第五个加 9 块；第六个加 11 块；第七个加 13 块。

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