1 . 已知数列
是等比数列,以下结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
A.![]() |
B.若![]() ![]() ![]() |
C.若![]() ![]() |
D.若数列![]() ![]() ![]() |
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解题方法
2 . 已知公差大于0的等差数列
的前
项和为
,
,且
,
,
成等比数列.
(1)求
的通项公式及
;
(2)设数列
的前
项和为
,求数列
中整数的个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.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/190303fa2246dac9d0e551a0aeb4b4c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5da4cd81500bdb43118150dbdb1541e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d51fbd012cde151c2b0f84e6b15e09aa.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5d982eac06ee4982afa243bdf99e77f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de777c4e44546bcfe26ad5b6bb418052.png)
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3 . 已知等比数列
的前
项积为
,
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7941c37db7309401a6aa8322667f02fc.png)
A.![]() | B.![]() |
C.![]() | D.若![]() ![]() |
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4 . 已知等比数列
的前
项和为
,且
,若
,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.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/e9645bd4d2002993b90ec6d48f9c04f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d81ec81c0b0946ffbd838722065adc9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b7b58766b2c48e1771229d2457b2674.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4da13d38b5bfe409ad174de50a3faabe.png)
A.27 | B.45 | C.65 | D.73 |
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名校
5 . 记
为数列
的前n项和,若
,且
,
,
成等比数列,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2180801cb6bd964133351fe5e7cd78e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fd71bc7e6668f90f259ad0b06dd60c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc858b7a95c5006a44067022da09f667.png)
A.![]() | B.![]() |
C.![]() ![]() ![]() | D.![]() |
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6 . 已知公差不为零的等差数列
满足:
,且
成等比数列,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a0bfa56250f5308110c2e9add97e0fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29b1b845916a4b6a18cdfbcd308d09c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f5eb9b8f893dd71876349ad40724550.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
7 . 若
,
,
成等比数列,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8401bb16895bde1550fb7cb6047c777d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0185be1f1c6717d1580527bfd3944f58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
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8 . 已知数列
是公差不为零的等差数列,
且
,
,
成等比数列.
(1)求数列
的通项公式;
(2)设数列
的前n项和为
,在①
,
; ②
,
;③
,
;这三个条件中任选一个,将序号补充在下面横线处,并根据题意解决问题.问题:若
,且______,求数列
的前n项和
.
(注:如果选择多个条件分别解答,按第一个解答给分.)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65fc200f10b97588a0c9896277c9c64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be9c9b05fd84ac9256d49a5a553af5.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b75dbb20178da2eec9ff11a9c74e841.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fc93bdea0b85a84179354b598b6f74e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a79df6b501e8be189ef89bd39c000a4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c394d7bd6be49f089aa78d2d4fd0a9cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
(注:如果选择多个条件分别解答,按第一个解答给分.)
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9 . 若
,b,c为实数,数列
是等比数列,则b的值为__________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e08d9b00f1b9368c88684a5dd79db13.png)
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解题方法
10 . 在数列
中,
,
,
且
.
(1)设
,证明:
是等比数列;
(2)设
为数列
的前
项和,是否存在互不相等的正整数
满足
,且
,
,
成等比数列?若存在,求出所有满足要求的
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ecf69901899bba130968c7a091790d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ab965b63c10ec92f8235f0faa5919b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97769855336d73371930df1f187875e.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fdb50cacd8eb999c9398a3ec378b416.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eaac721898793d14a799c79db3658685.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc198dee35459651ae1cc73b01be08cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11de7912c83c0eca21eb84e126050b0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66acc93c1a14651caf3e39d20ff83bf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/938c5894c71c8f4d08674250429d88ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eaac721898793d14a799c79db3658685.png)
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