1 . 等比数列的前
项和
已知
为等比数列且公比为
,
为其前
项和.
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61b7a07ade5913a6e6b54dbf1c23a5f3.png)
________ 或者![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d0980e3f744e203ae45c4bbb442e336.png)
________
(2)我们用方法________ 推导
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61b7a07ade5913a6e6b54dbf1c23a5f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d0980e3f744e203ae45c4bbb442e336.png)
(2)我们用方法
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
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2 . 等比数列的性质
已知
为等比数列,公比为
,
为其前
项和.
(1)若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8647b84bfbc7d827f56be74888b9fdb6.png)
______ ;
(2)当
时,
,________ ,
为等比数列;
(3)若等比数列
共
项,记
为诸奇数项和,
为诸偶数项和,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/186fad5c3b123434e46e02c26dcc3c32.png)
____ ;
已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c618d7069d2e18c8164ed0e6fa7811f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8647b84bfbc7d827f56be74888b9fdb6.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1d236a265a6cc0f3d06a0e568ffa907.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7ce01c8a13621ad26ea353b067dfaa8.png)
(3)若等比数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b5631bc01b998a4b3fabd9e131699dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9df956d8d43778655131703be9ad9a41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16ce99d82b6ad34142c6920031a454e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/186fad5c3b123434e46e02c26dcc3c32.png)
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3 . 等比数列的前
项和
已知
为等比数列且公比为
,
为其前
项和.
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c2864e2ec3416cc4c081ac1f71a0af.png)
____________ 或者![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c2864e2ec3416cc4c081ac1f71a0af.png)
___________ .
(2)我们用方法_______________ 推导
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c2864e2ec3416cc4c081ac1f71a0af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c2864e2ec3416cc4c081ac1f71a0af.png)
(2)我们用方法
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
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23-24高二上·江苏·课后作业
4 . 等比数列的通项公式
若
为等比数列,公比为
.
(1)
的通项公式为_______ ,
(2)
为递增数列的充要条件为_____ ;
为递减数列的充要条件为_____ ;
为常数列的充要条件为______ .
若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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23-24高二上·江苏·课后作业
5 . 等比数列的定义
(1)一般地,如果一个数列从第二项起,每一项与它的前一项所得的比都等于___ ,那么这个数列就叫作等比数列,这个常数叫作等比数列的公比,通常用
表示.
(2)如果数列
满足
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ff3f9ee4c62803165f629bd03497e3.png)
_______ ,则
为等比数列.
(1)一般地,如果一个数列从第二项起,每一项与它的前一项所得的比都等于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
(2)如果数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffa01f03fb074bff35b35e07047d11b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ff3f9ee4c62803165f629bd03497e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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