（5分）如图程序框图是为了求出满足 3^ n -2^ n…——2017 高考数学第 10 题答案解析

2017_新课标 I 卷 (2017·文)

2017 ?? 第 10 题 单选题 区分题
2017_新课标 I 卷 (2017·文)

10．（5分）如图程序框图是为了求出满足 $3^{n}-2^{n}>1000$ 的最小偶数 $n$ ，那么在

和 □两个空白框中，可以分别填入（ ）

A. $A>1000$ 和 $n=n+1$
B. $A>1000$ 和 $n=n+2$
C. $A \leq 1000$ 和 $n=n+1$
D. $A \leq 1000$ 和 $n=n+2$
参考答案D
查看原卷 →

完整解析 · 逐步详解

【考点】EF：程序框图．
【专题】11：计算题；38：对应思想；49：综合法；5K：算法和程序框图．

【分析】通过要求 $\mathrm{A}>1000$ 时输出且框图中在＂否＂时输出确定＂
<img class="imgSvg" id = "motsgms4tju148piz8" src="data:image/svg+xml;base64,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"/>
＂内不能输入＂ $\mathrm{A}>1000$＂，进而通过偶数的特征确定 $\mathrm{n}=\mathrm{n}+2$ ．

【解答】解：因为要求 $\mathrm{A}>1000$ 时输出，且框图中在＂否＂时输出，

所以＂
<img class="imgSvg" id = "motsgms8epf80e2qzr" src="data:image/svg+xml;base64,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"/>
＂内不能输入＂A＞1000＂，

又要求 $n$ 为偶数，且 $n$ 的初始值为 0 ，

所以＂ □ ＂中 n 依次加 2 可保证其为偶数，

所以 D 选项满足要求，
故选：D．
【点评】本题考查程序框图，属于基础题，意在让大部分考生得分．

✅ 来源：2017年 · ?? · 2017_新课标 I 卷 (2017·文) · 第 10 题 · 本题已通过人工审核与系统自动校验

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