已知等差數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024615510481.png)
中,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024615526429.png)
;
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024615541334.png)
是
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024615557344.png)
與
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024615557356.png)
的等比中項(xiàng).
(I)求數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024615510481.png)
的通項(xiàng)公式:
(II)若
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024615588505.png)
.求數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024615604604.png)
的前
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024615619297.png)
項(xiàng)和.
(I)當(dāng)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024615635412.png)
時(shí),
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024615651432.png)
;當(dāng)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024615666416.png)
時(shí),
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024615666527.png)
;(II)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024615682798.png)
.
試題分析:(I)通過已知
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024615713348.png)
,可以設(shè)公差為
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024615729321.png)
,然后根據(jù)等比中項(xiàng)的概念列出等式
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024615744862.png)
解出公差
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024615635412.png)
或
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024615775291.png)
,所以當(dāng)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024615635412.png)
時(shí),
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024615651432.png)
;當(dāng)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024615666416.png)
時(shí),
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024615666527.png)
;(II)根據(jù)條件可以確定
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024615838348.png)
的通項(xiàng)公式
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024615666527.png)
,則
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024615869641.png)
,然后用錯(cuò)位相減法解出
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024615682798.png)
.
試題解析:(I)由題意,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024615900530.png)
,即
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024615744862.png)
,化簡(jiǎn)得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024615931561.png)
,∴
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024615635412.png)
或
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024615775291.png)
∵
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024615963432.png)
,∴當(dāng)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024615635412.png)
時(shí),
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024615651432.png)
;當(dāng)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024615666416.png)
時(shí),
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024615666527.png)
.
(II)∵
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024616041507.png)
,∴
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024615666527.png)
,∴
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024615869641.png)
,∴
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024616087966.png)
……①
①
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024616087214.png)
2,得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240246161031048.png)
……②,①-②,得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024616134968.png)
=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024616150870.png)
,∴
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024615682798.png)
.
練習(xí)冊(cè)系列答案
相關(guān)習(xí)題
科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
已知等比數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031353559471.png)
的公比為
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031353575310.png)
,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031353590388.png)
是
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031353559471.png)
的前
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031353606297.png)
項(xiàng)和.
(1)若
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031353621370.png)
,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031353637390.png)
,求
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031353653686.png)
的值;
(2)若
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031353621370.png)
,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031353668406.png)
,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031353590388.png)
有無最值?并說明理由;
(3)設(shè)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031353699456.png)
,若首項(xiàng)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031353715314.png)
和
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031353731267.png)
都是正整數(shù),
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031353731267.png)
滿足不等式:
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031353746605.png)
,且對(duì)于任意正整數(shù)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031353606297.png)
有
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031353777626.png)
成立,問:這樣的數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031353559471.png)
有幾個(gè)?
查看答案和解析>>
科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
已知數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025738370473.png)
為等差數(shù)列,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025738386388.png)
為其前
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025738417297.png)
項(xiàng)和,且
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025738433721.png)
(1)求數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025738370473.png)
的通項(xiàng)公式;(2)求證:數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025738479557.png)
是等比數(shù)列;
查看答案和解析>>
科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
已知點(diǎn)(1,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024501441324.png)
)是函數(shù)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024501457730.png)
且
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024501472376.png)
)的圖象上一點(diǎn),等比數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024501488457.png)
的前
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024501504277.png)
項(xiàng)和為
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024501519549.png)
,數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024501535475.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024501550556.png)
的首項(xiàng)為
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024501566237.png)
,且前
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024501504277.png)
項(xiàng)和
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024501597388.png)
滿足
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024501597388.png)
-
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024501628426.png)
=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024501644449.png)
+
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024501660488.png)
(
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024501660435.png)
).
(1)求數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024501488457.png)
和
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024501535475.png)
的通項(xiàng)公式;
(2)求數(shù)列{
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024501706590.png)
前
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024501504277.png)
項(xiàng)和為
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024501738373.png)
,問
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024501738373.png)
>
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024501769537.png)
的最小正整數(shù)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024501504277.png)
是多少?
查看答案和解析>>
科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
已知數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024331897456.png)
滿足
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024331913771.png)
(1)求
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024331897456.png)
的通項(xiàng)公式;
(2)證明:
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024331928760.png)
.
查看答案和解析>>
科目:高中數(shù)學(xué)
來源:不詳
題型:填空題
在各項(xiàng)均為正數(shù)的等比數(shù)列{an}中,已知a1+a2+a3=2,a3+a4+a5=8,則a4+a5+a6= .
查看答案和解析>>
科目:高中數(shù)學(xué)
來源:不詳
題型:填空題
設(shè)等比數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824023810942456.png)
滿足公比
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824023810958512.png)
,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824023810973555.png)
,且{
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824023810989345.png)
}中的任意兩項(xiàng)之積也是該數(shù)列中的一項(xiàng),若
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824023811004479.png)
,則
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824023811020304.png)
的所有可能取值的集合為
.
查看答案和解析>>
科目:高中數(shù)學(xué)
來源:不詳
題型:單選題
在等比數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024927546456.png)
中,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024927562870.png)
,則公比
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024927578310.png)
等于( )
A.2 | B.![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024927593338.png) | C.-2 | D.![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024927609363.png) |
查看答案和解析>>