AMC 8 2005 Problem 12
AMC8 2005 年第 12 题
数列与规律★★★☆☆
Big Al, the ape, ate 100 bananas from May 1 through May 5. Each day he ate six more bananas than on the previous day. How many bananas did Big Al eat on May 5?
从 5 月 1 日到 5 月 5 日，Big AL 这只大猩猩共吃了 100 根美味的黄香蕉。他每天比前一天多吃六根香蕉。那么它在 5 月 5 日这天吃了多少根美味的香蕉？
- A.20
- B.22
- C.30
- D.32
- E.34
正确答案 · Correct Answer
D
解析 · Solution
Solution 1
There are 5 days from May 1 to May 5. The number of bananas he eats each day is an arithmetic sequence. He eats bananas on May 5, and n-4(6)=n-24 bananas on May 1. The sum of this arithmetic sequence is equal to 100. $$$$$$$$
There are 5 days from May 1 to May 5. If we set the first day as , the second day can be expressed as n+6, the third as n+12, and so on, for five days. The sum n+(n+6)+(n+12)+(n+18)+(n+24) is equal to 100, as stated in the problem. We can write a very simple equation, that is: 5n+60 = 100. Now all we do is just solve. 5n = 40, so Big Al eats 8 bananas on the first day. The fifth day, n+24, is then 32, which is your answer. Simply realize that the middle term of the arithmetic sequence is the arithmetic mean of all terms, which is simply . This means that the number of bananas the ape ate on May 5th is just 20+6*2 = 32. Select . You can do this quicker than you read it if you truly master arithmetic sequences.
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