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【319500】【详解】三年级(上)第22讲 等差数列应用

时间:2025-01-07 22:54:07 作者: 字数:2184字
简介:
试题简介

本试卷主要围绕“等差数列应用”展开,考察范围包括等差数列的求和公式、等差数列的性质以及实际应用。试题难度适中,例题和练习题多为基础题,如简单的求和问题、连续自然数的和等,旨在巩固学生对等差数列基本概念和公式的理解;同时也有一定综合性的题目,如等差数列的公差和首项求解、分数更正问题等,考查学生的分析和应用能力。亮点在于结合生活场景和实际问题,如考试分数、连续自然数等,增强试题的趣味性和实用性,同时通过多样化的题型,培养学生的逻辑思维和解决问题能力。

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第二十二讲 等差数列应用

  1. 例题1
    答案:3
    详解:先求出第4项: <a href="/tags/221/" title="等差数列" class="c1" target="_blank">等差数列</a> <a href="/tags/162/" title="数列" class="c1" target="_blank">数列</a> ,所以公差为: <a href="/tags/221/" title="等差数列" class="c1" target="_blank">等差数列</a> <a href="/tags/162/" title="数列" class="c1" target="_blank">数列</a> ,第10项为: <a href="/tags/221/" title="等差数列" class="c1" target="_blank">等差数列</a> <a href="/tags/162/" title="数列" class="c1" target="_blank">数列</a>

  2. 例题2
    答案:10
    详解:9个连续自然数是一个公差为1的等差数列,第5项为: <a href="/tags/221/" title="等差数列" class="c1" target="_blank">等差数列</a> <a href="/tags/162/" title="数列" class="c1" target="_blank">数列</a> ,所以最小的数为: <a href="/tags/221/" title="等差数列" class="c1" target="_blank">等差数列</a> <a href="/tags/162/" title="数列" class="c1" target="_blank">数列</a>

  3. 例题3
    答案:39
    详解:先根据前15项之和,求出第8项为: <a href="/tags/221/" title="等差数列" class="c1" target="_blank">等差数列</a> <a href="/tags/162/" title="数列" class="c1" target="_blank">数列</a> .再根据21项之和,求出第11项为: <a href="/tags/221/" title="等差数列" class="c1" target="_blank">等差数列</a> <a href="/tags/162/" title="数列" class="c1" target="_blank">数列</a> .所以公差是: <a href="/tags/221/" title="等差数列" class="c1" target="_blank">等差数列</a> <a href="/tags/162/" title="数列" class="c1" target="_blank">数列</a> ,首项为: <a href="/tags/221/" title="等差数列" class="c1" target="_blank">等差数列</a> <a href="/tags/162/" title="数列" class="c1" target="_blank">数列</a>

  4. 例题4
    答案:38
    详解:8个连续偶数构成的是公差为2的一个等差数列,最大数应该比最小数大 <a href="/tags/221/" title="等差数列" class="c1" target="_blank">等差数列</a> <a href="/tags/162/" title="数列" class="c1" target="_blank">数列</a> ,再算出最小数与最大数的和: <a href="/tags/221/" title="等差数列" class="c1" target="_blank">等差数列</a> <a href="/tags/162/" title="数列" class="c1" target="_blank">数列</a> ,所以最大数为: <a href="/tags/221/" title="等差数列" class="c1" target="_blank">等差数列</a> <a href="/tags/162/" title="数列" class="c1" target="_blank">数列</a>

  5. 例题5
    答案:39
    详解:“前15项之和为450”,所以第1项与第15项之和为: <a href="/tags/221/" title="等差数列" class="c1" target="_blank">等差数列</a> <a href="/tags/162/" title="数列" class="c1" target="_blank">数列</a> .同样地,算出第1项与第20项之和为75,都含有第1项,所以第20项比第15项大了 <a href="/tags/221/" title="等差数列" class="c1" target="_blank">等差数列</a> <a href="/tags/162/" title="数列" class="c1" target="_blank">数列</a> ,公差为: <a href="/tags/221/" title="等差数列" class="c1" target="_blank">等差数列</a> <a href="/tags/162/" title="数列" class="c1" target="_blank">数列</a> ,第15项比首项大 <a href="/tags/221/" title="等差数列" class="c1" target="_blank">等差数列</a> <a href="/tags/162/" title="数列" class="c1" target="_blank">数列</a> ,所以首项为: <a href="/tags/221/" title="等差数列" class="c1" target="_blank">等差数列</a> <a href="/tags/162/" title="数列" class="c1" target="_blank">数列</a>

  6. 例题6
    答案:99
    详解:原来是最低的,加了21分之后应该变成最高的,公差是3,所以小组里共有7人.原来中间的数为 <a href="/tags/221/" title="等差数列" class="c1" target="_blank">等差数列</a> <a href="/tags/162/" title="数列" class="c1" target="_blank">数列</a> 分,所以最后小高是99分.

  7. 练习1
    答案:60
    简答:第6项为: <a href="/tags/221/" title="等差数列" class="c1" target="_blank">等差数列</a> <a href="/tags/162/" title="数列" class="c1" target="_blank">数列</a> ,公差为: <a href="/tags/221/" title="等差数列" class="c1" target="_blank">等差数列</a> <a href="/tags/162/" title="数列" class="c1" target="_blank">数列</a> ,第20项为: <a href="/tags/221/" title="等差数列" class="c1" target="_blank">等差数列</a> <a href="/tags/162/" title="数列" class="c1" target="_blank">数列</a>

  8. 练习2
    答案:7
    简答:第4个是: <a href="/tags/221/" title="等差数列" class="c1" target="_blank">等差数列</a> <a href="/tags/162/" title="数列" class="c1" target="_blank">数列</a> ,最小数为7

  9. 练习3
    答案:11
    简答:第7项为: <a href="/tags/221/" title="等差数列" class="c1" target="_blank">等差数列</a> <a href="/tags/162/" title="数列" class="c1" target="_blank">数列</a> ,第8项为: <a href="/tags/221/" title="等差数列" class="c1" target="_blank">等差数列</a> <a href="/tags/162/" title="数列" class="c1" target="_blank">数列</a> ,公差为5,则首项为: <a href="/tags/221/" title="等差数列" class="c1" target="_blank">等差数列</a> <a href="/tags/162/" title="数列" class="c1" target="_blank">数列</a>

  10. 练习4
    答案:7
    简答:最小数比最大数小9,且最小数与最大数之和为: <a href="/tags/221/" title="等差数列" class="c1" target="_blank">等差数列</a> <a href="/tags/162/" title="数列" class="c1" target="_blank">数列</a> ,则最小数为7

  11. 作业1
    答案:37
    简答:第4项为 <a href="/tags/221/" title="等差数列" class="c1" target="_blank">等差数列</a> <a href="/tags/162/" title="数列" class="c1" target="_blank">数列</a> ,而首项为17,那么公差为 <a href="/tags/221/" title="等差数列" class="c1" target="_blank">等差数列</a> <a href="/tags/162/" title="数列" class="c1" target="_blank">数列</a> ,第11项为 <a href="/tags/221/" title="等差数列" class="c1" target="_blank">等差数列</a> <a href="/tags/162/" title="数列" class="c1" target="_blank">数列</a>

  12. 作业2
    答案:10
    简答:中间项即第4个数为 <a href="/tags/221/" title="等差数列" class="c1" target="_blank">等差数列</a> <a href="/tags/162/" title="数列" class="c1" target="_blank">数列</a> ,则最小的是10

  13. 作业3
    答案:7
    简答: <a href="/tags/221/" title="等差数列" class="c1" target="_blank">等差数列</a> <a href="/tags/162/" title="数列" class="c1" target="_blank">数列</a> ,所以 <a href="/tags/221/" title="等差数列" class="c1" target="_blank">等差数列</a> <a href="/tags/162/" title="数列" class="c1" target="_blank">数列</a> ,而对于8个连续奇数,末项比首项大 <a href="/tags/221/" title="等差数列" class="c1" target="_blank">等差数列</a> <a href="/tags/162/" title="数列" class="c1" target="_blank">数列</a> ,则首项为7

  14. 作业4
    答案:28
    简答:这10个连续自然数构成一个公差为1的等差数列, <a href="/tags/221/" title="等差数列" class="c1" target="_blank">等差数列</a> <a href="/tags/162/" title="数列" class="c1" target="_blank">数列</a> ,所以 <a href="/tags/221/" title="等差数列" class="c1" target="_blank">等差数列</a> <a href="/tags/162/" title="数列" class="c1" target="_blank">数列</a> ,而首项又比末项小9,则首项为28

  15. 作业5
    答案:11
    简答:第6项为 <a href="/tags/221/" title="等差数列" class="c1" target="_blank">等差数列</a> <a href="/tags/162/" title="数列" class="c1" target="_blank">数列</a> ,第10项为 <a href="/tags/221/" title="等差数列" class="c1" target="_blank">等差数列</a> <a href="/tags/162/" title="数列" class="c1" target="_blank">数列</a> ,则公差为 <a href="/tags/221/" title="等差数列" class="c1" target="_blank">等差数列</a> <a href="/tags/162/" title="数列" class="c1" target="_blank">数列</a> ,首项为 <a href="/tags/221/" title="等差数列" class="c1" target="_blank">等差数列</a> <a href="/tags/162/" title="数列" class="c1" target="_blank">数列</a>

 

 

 

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