AMC8 2013

AMC8 2013 · Q9

AMC8 2013 · Q9. It mainly tests Exponents & radicals, Sequences & recursion (algebra).

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?

绿巨人每次跳跃的距离都能翻倍。如果第一次跳 1 米，第二次 2 米，第三次 4 米，以此类推，他在第几次跳跃中第一次能跳超过 1 公里？

(A) 9th 第 9 次

(B) 10th 第 10 次

(D) 12th 第 12 次

(E) 13th 第 13 次

Answer

Correct choice: (C)

正确答案：（C）

Solution

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 $10-0+1=\boxed{\textbf{(C)}\ 11^{\text{th}}}$

这是一个公比为 2 的等比数列。要找到超过 1000 米的跳跃，注意到$2^{10}=1024$。但由于首项是$2^0=1$而不是$2^1=2$，因此解为$10-0+1=\boxed{\textbf{(C)}\ 11^{\text{th}}}$。

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