名校
1 . 如图,第1个图形需要4根火柴,第2个图形需要7根火柴,
,设第n个图形需要
根火柴.
![](https://img.xkw.com/dksih/QBM/2022/1/20/2898670031757312/2908679870808064/STEM/cbefc279-2a3e-4232-9266-fcebe7c364a8.png?resizew=486)
(1)试写出
,并求
;
(2)记前n个图形所需的火柴总根数为
,设
,求数列
的前n项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dab783880d7aabc422916886630fc576.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://img.xkw.com/dksih/QBM/2022/1/20/2898670031757312/2908679870808064/STEM/cbefc279-2a3e-4232-9266-fcebe7c364a8.png?resizew=486)
(1)试写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(2)记前n个图形所需的火柴总根数为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1606dd20b4b2460ee0807d7f2ee6277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1a208706fe64c4a6709e9de5da2bdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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2022-02-03更新
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