AMC 8 2013 Problem 9

AMC8 2013 年第 9 题

数列与规律★★☆☆☆

The Incredible Hulk can double the distance he jumps with each succeeding jump. If his first jump is 1 meter, the second jump is 2 meters, the third jump is 4 meters, and so on, then on which jump will he first be able to jump more than 1 kilometer (1,000 meters)?

绿巨人浩克每次跳的长度都是前面一次的两倍。若它第一次跳了 1 米，第二次跳了 2 米，第三次跳了 4 米，以此类推，那么第几次跳的长度超过 1 公里？

A.9-th
B.10-th
C.11-th
D.12-th
E.13-th

正确答案 · Correct Answer

解析 · Solution

Solution 1

This is a geometric sequence in which the common ratio is 2. To find the jump that would be over a 1000 meters, we note that

2^{10}=1024

. However, because the first term is

2^0=1

and not

2^1=2

, the solution to the problem is

10-0+1=11^{\text{th}}

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