AMC12 2004 B

AMC12 2004 B · Q8

AMC12 2004 B · Q8. It mainly tests Arithmetic sequences basics, Basic counting (rules of product/sum).

A grocer makes a display of cans in which the top row has one can and each lower row has two more cans than the row above it. If the display contains $100$ cans, how many rows does it contain?

某杂货商用罐头摆成展示：最上面一行有一个罐头，并且每往下一行比上一行多两个罐头。若该展示共有 $100$ 个罐头，它共有多少行？

(A) 5 5

(B) 8 8

(D) 10 10

(E) 11 11

Answer

Correct choice: (D)

正确答案：（D）

Solution

The sum of the first $n$ odd numbers is $n^2$. As in our case $n^2=100$, we have $n=\boxed{\mathrm{(D)\ }10}$.

前 $n$ 个奇数之和为 $n^2$。在本题中 $n^2=100$，因此 $n=\boxed{\mathrm{(D)\ }10}$。

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