解题方法
1 . 判断正误(正确的填“正确”,错误的填“错误”)
(1)当
时,
为递增数列.( )
(2)当
时,
为常数列.( )
(3)
是等比数列,若
,则
.( )
(4)若等比数列
的公比是
,则
(
).( )
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eda6dc559d07bc22c9a0ed1e3a6d01d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfa9bf65189dfb57a61644a1cb27f361.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd9b26b74b54a192806097b698fac864.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17d2e59aeab922d37da08fd7c9f517ba.png)
(4)若等比数列
![](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/661f8c3fabb7391571e555c2d325ab81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d38b6286e5f74b604b9fb639c55d611f.png)
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解题方法
2 . 判断正误(正确的写正确,错误的写错误)
(1)求等比数列
的前n项和时可直接套用公式
来求.( )
(2)首项为a的数列既是等差数列又是等比数列,则其前n项和为
.( )
(3)若某数列的前n项和公式为
,则此数列一定是等比数列.( )
(4)若数列
的前n项和
,则数列
不是等比数列.( )
(1)求等比数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbdcb1e2554b4dc87359ba028c79c504.png)
(2)首项为a的数列既是等差数列又是等比数列,则其前n项和为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1750a296a35fd6a5ea68e982ae6fc975.png)
(3)若某数列的前n项和公式为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dd95eaff081923ceeff6b74d62ccef8.png)
(4)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1d93da1921383b3932de3363f17184.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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3 . 判断正误(正确的写正确,错误的写错误)
(1)递推公式也是表示数列的一种方法.( )
(2)所有数列都有递推公式.( )
(3)仅由数列
的关系式
就能确定这个数列.( )
(4)
化简后关于n与
的函数式即为数列
的通项公式.( )
(1)递推公式也是表示数列的一种方法.
(2)所有数列都有递推公式.
(3)仅由数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f55c8b53b20f72495a965a0e3d82b661.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afb3a38dcbf49f46dadc2e3b6fcaf9d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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4 . 判断正误(正确的写正确,错误的写错误)
(1)若一个数列从第二项起每一项与前一项的比为常数,则该数列为等比数列.( )
(2)等比数列的首项不能为零,但公比可以为零.( )
(3)常数列一定为等比数列.( )
(4)任何两个数都有等比中项.( )
(1)若一个数列从第二项起每一项与前一项的比为常数,则该数列为等比数列.
(2)等比数列的首项不能为零,但公比可以为零.
(3)常数列一定为等比数列.
(4)任何两个数都有等比中项.
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5 . 判断正误(正确的打“正确”,错误的打“错误”)
(1)若
是等差数列,则
也是等差数列.( )
(2)若
是等差数列,则
也是等差数列.( )
(3)若
是等差数列,则对任意
都有
.( )
(4)等差数列
不是递增数列就是递减数列.( )
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b91adba8efbf964e9e35547b0fd0ea36.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b91adba8efbf964e9e35547b0fd0ea36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68b93bb2c66e49ac3efaf0686d4f3815.png)
(4)等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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解题方法
6 . 判断正误(正确的填“正确”,错误的填“错误”)
(1)等差数列的前n项和一定是项数n的二次函数.( )
(2)若等差数列
的公差为d,前n项和为
.则
的公差为
.( )
(3)若数列
的前n项和
,则
不是等差数列.( )
(4)等差数列
的前n项和
,
可能是等差数列.( )
(1)等差数列的前n项和一定是项数n的二次函数.
(2)若等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dea1dd4ffcb4cf0697ca43079f6a1f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c9823c2429d3867217d283dba4bf042.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3d2dd8cb8712c7890b14cf5beedf17f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(4)等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/846fa57d92d6ad44d6a0cafad1e71ed4.png)
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7 . 判断正误(正确的填“正确”,错误的填“错误”)
(1)数列1,1,1,1,1是等差数列.( )
(2)若一个数列从第2项起每一项与前一项的差都是常数,则这个数列是等差数列.( )
(3)任意两个实数都有等差中项.( )
(4)等差数列的公差是相邻两项的差.( )
(1)数列1,1,1,1,1是等差数列.
(2)若一个数列从第2项起每一项与前一项的差都是常数,则这个数列是等差数列.
(3)任意两个实数都有等差中项.
(4)等差数列的公差是相邻两项的差.
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8 . 判断正误(正确的写正确,错误的写错误)
(1)数列
和数列
是同一个数列.( )
(2)数列中的每一项都与它的序号有关.( )
(3)
与
是不同的概念.( )
(4)有些数列没有通项公式.( )
(1)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66265fdf44defb54192cecb9349a26b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95a498a5503156a4485b95c0da967e66.png)
(2)数列中的每一项都与它的序号有关.
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cee766a75ae9ee290e403b42b3569db6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87e38321617930485aed7b188a22f464.png)
(4)有些数列没有通项公式.
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9 . 判断正误(正确的填“正确”,错误的填“错误”)
(1)
是一元二次不等式.( )
(2)若方程
没有实数根,则不等式
的解集为
.( )
(3)设二次方程
的两实数根为
,则一元二次不等式
的解集不可能为
.( )
(4)
的解集可能是
.( )
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a8eb9e90617834d53b7755e518ce2eb.png)
(2)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24527361966ba6ded458eed6bcee59df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a42c345443ea8da6d1b73b4035e2566d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
(3)设二次方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7380b4cd6434b4b458d711826e49d23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a42c345443ea8da6d1b73b4035e2566d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2227e27e8d34198f022bf7024503cb0a.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a42c345443ea8da6d1b73b4035e2566d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/574bdac28b1dcbf03f0fb903e8d0b49a.png)
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10 . 判断正误(正确的填“正确”,错误的填“错误”)
(1)两个不等式
与
成立的条件是相同的.( )
(2)当
时,
.( )
(3)当
时,
.( )
(4)函数
的最小值是2.( )
(1)两个不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48fe5d9cbe4f83926f5c21912df67a2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/689f982af451283289255c87593ec338.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2684b72f9f38f5046c8ecd4280b7b14b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/759c09917e5728d75bf5cfdb5b4a807f.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2684b72f9f38f5046c8ecd4280b7b14b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf3827ed33eeca93ecd65f9633de230d.png)
(4)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1305b9abebd7bef3171486df157286b3.png)
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