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1 . 如图甲是第七届国际数学教育大会(简称
)的会徽图案,会徽的主体图案是由如图乙的一连串直角三角形演化而成的,其中
,如果把图乙中的直角三角形继续作下去,记
、
、
、
、
的长度构成数列
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42e4487468ab2823d6dbf7f0ebd2eb38.png)
______ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0184d9ea233cd7983be93fe160d19ad9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b76509f4dc5e40d45665e929267a5ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4195334905e2f190f958dbf5951456f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48e28a84838f722c8233987a73e0257c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/337d0dc1076cfdb02ffb40bf4dac0d90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42e4487468ab2823d6dbf7f0ebd2eb38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
![](https://img.xkw.com/dksih/QBM/2020/6/15/2485419465760768/2485871001124864/STEM/dcfbdb32664c43cda984038bba09989a.png?resizew=460)
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2 . 已知函数
,若对于数列
满足:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fb9f395447d0edc38904389520d237d.png)
,且
.
(1)求证:数列![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a77eb01fb0dfdd6f1e7ca28ceb7ff775.png)
为等差数列,并求数列
的通项公式;
(2)设
,若数列
的前
项和为
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c17ccdb6155f481fd5a5c262b8fc2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fb9f395447d0edc38904389520d237d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c84dde52d49ed2662f230378cc27ddf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea7892d6b8810c8e5273e36d7a966f24.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a77eb01fb0dfdd6f1e7ca28ceb7ff775.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c84dde52d49ed2662f230378cc27ddf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d464b6aab7f85f04a5fff2daa72ea12b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
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3 . 将正奇数1,3,5,7,…,排成五列(如表),按此表的排列规律,89所在的位置是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/10/8eb18b16-a0d5-479d-8920-6c7ebf0550df.png?resizew=149)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/10/8eb18b16-a0d5-479d-8920-6c7ebf0550df.png?resizew=149)
A.第一列 | B.第二列 | C.第三列 | D.第四列 |
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