解题方法
1 . 若数列{an}满足a1=1,an+1=2an(n∈N*),则a4=________ ,前8项的和S8=________ .
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23-24高二下·全国·课前预习
2 . 知识点05等比数列的性质
1、“子数列”性质
(1)对于无穷等比数列
,若将其前
项去掉,剩余各项仍为等比数列,首项为
,公比为
;
若取出所有的
的倍数项,组成的数列仍为等比数列,首项为
,公比为
;
(2)相隔等距离的项组成的数列仍是等比数列,即
仍是等比数列,公比为 ____ ![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7ee88f532329c9fbc70d6c544497292.png)
2、“下标和”性质:在等比数列
中,若
,则____ ;
(1)特别地,
时,____ ;
当
时,____
(2)若数列
是有穷数列,则与首末两项“等距离”的两项的积等于首末两项的积,即![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4ddaf21329cb1824329c296eaad5336.png)
3、两等比数列合成数列的性质:若数列
是项数相同的等比数列,
是不等于0的常数,则数列
也是____ .
1、“子数列”性质
(1)对于无穷等比数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/217b927efe12a98e1082ecd7f035b921.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
若取出所有的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f255d0395fba51ca2d44293cca42e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e248261e3017741f15614caea31d0ce0.png)
(2)相隔等距离的项组成的数列仍是等比数列,即
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b7802fa4893785d5a8f6ea1edb8cffe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7ee88f532329c9fbc70d6c544497292.png)
2、“下标和”性质:在等比数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f0c04bf4f330778a67c31371c5cf64.png)
(1)特别地,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d35a47bf120bdc9294da261220947532.png)
当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/865b6be02589dde9a2fb834ee7b8004b.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4ddaf21329cb1824329c296eaad5336.png)
3、两等比数列合成数列的性质:若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed48c3e5c53eba20c2e262b7d2c09bfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50e60f14235ca70ecc310820a747a548.png)
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