AMC 8 2016 Problem 19
AMC8 2016 年第 19 题
数列与规律★★★☆☆
The sum of 25 consecutive even integers is 10,000 . What is the largest of these 25 consecutive integers?
25 个连续的偶数之和是 10,000，问这 25 个连续的整数中，最大的数是多少？
- A.360
- B.388
- C.412
- D.416
- E.424
正确答案 · Correct Answer
E
解析 · Solution
Solution 1
Let be the 13th consecutive even integer that's being added up. By doing this, we can see that the sum of all 25 even numbers will simplify to since . Now, . Remembering that this is the 13th integer, we wish to find the 25th, which is 400+2(25-13)=424.
Let be the smallest number. The equation will become, . After you combine like terms, you get 25x+(50*12)=10,000 which turns into 10,000-600=25x. 25x=9400, so x=376. Then, you add 376+48 = 424. Edit(dnathan12): For clarity, you add 48, because you want the largest number in the list. 376 is the smallest number
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