AMC 8 2016 Problem 8
AMC8 2016 年第 8 题
数列与规律★★☆☆☆
Find the value of the expression: .
计算下面表达式的值
- A.20
- B.40
- C.50
- D.80
- E.100
正确答案 · Correct Answer
C
解析 · Solution
Solution 1
We can group each subtracting pair together: After subtracting, we have: There are 50 even numbers, therefore there are even pairs. Therefore the sum is
Since our list does not end with one, we divide every number by 2 and we end up with We can group each subtracting pair together: There are now 25 pairs of numbers, and the value of each pair is 1. This sum is 25. However, we divided by 2 originally so we will multiply 2*25 to get the final answer of 50
Note: This solution is very similar to, but simplified. The value of the expression increases by 2 after every pair as shown: Pair 1: [100-98= 2 ] Pair 1 + 2: [2+96-94= 4 ] Pair 1 + 2 + 3: [4+92-90= 6 ] Since there is 25 pairs in the expression, the value will increase by two 25 times. Thus, the sum of the expression is
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