專(zhuān)題六數(shù)列第十八講數(shù)列的綜合應(yīng)用

1、專(zhuān)題六 數(shù)列第十八講 數(shù)列的綜合應(yīng)用一、選擇題1（2018浙江）已知EMBED Equation.DSMT4Equation.DSMT4，EMBED Equation.DSMT4若EMBED Equation.DSMT4，則EMBED Equation.DSMT4成等比數(shù)列，且EMBEDEMBED Equation.DSMT4EMBED Equation.DSMT4，EMBED Equation.DSMT4EMBED Equation.DSMT4EMBED Equation.DSMT4，EMBED Equation.DSMT4EMBED Equation.DSMT4EMBED Equation

2、.DSMT4若AEquation.DSMT4 CEquation.DSMT42（2015湖北）設(shè)EMBED Equation.DSMT4Equation.DSMT4則ABCD3成等比數(shù)列；q：EMBED Equation.DSMT4的必要條件的充分條件p：EMBED Equation.DSMT4EMBEDEMBEDEMBEDp是q的充分條件，但不是qp是q的必要條件，但不是qP是q的充分必要條件p既不是q的充分條件，也不是q的必要條件2014新課標(biāo)2）等差數(shù)列EMBED Equation.DSMT4的公差為 ，EMBEDEquation.DSMT4，EMBED Equation.DSMT4Eq

3、uation.DSMT4的前EMBED Equation.DSMT4AEMBED Equation.DSMT4 Equation.DSMT4D4（2014浙江）設(shè)函數(shù) ， ，記EMBED Equation.DSMT4EMBED Equation.DSMT4，ABC二、填空題5（2018江蘇）已知集合2，若EMBED Equation.DSMT4成等比數(shù)列，則EMBED項(xiàng)和EMBEDEquation.DSMT4 BEMBED Equation.DSMT4 CEMBED Equation.DSMT4EMBEDEMBED Equation.DSMT4則DEMBED Equation.DSMT4EMB

4、ED Equation.DSMT4EMBED記EMBED Equation.DSMT4將EMBED Equation.DSMT4的前EMBEDEquation.DSMT4的最小值為 是等差數(shù)列， 公差EMBEDEquation.DSMT4，EMBED Equation.DSMT4，EMBEDEquation.DSMT4，則EMBED Equation.DSMT4，Equation.DSMT4的所有元素從小到大依次排列構(gòu)成一個(gè)數(shù)列EMBED Equation.DSMT4為數(shù)列EMBEDEquation.DSMT4項(xiàng)和，則使得EMBED Equation.DSMT4成立的EMBED Equatio

5、n.DSMT4 6（2015浙江）已知EMBED Equation.DSMT4不為零若EMBED Equation.DSMT4成等比數(shù)列，且EMBED Equation.DSMT4EMBED Equation.DSMT47（2013重慶）已知 是等差數(shù)列，8（2011江蘇）Equation.DSMT4 Equation.DSMT4三、解答題9（2018江蘇）EMBEDEquation.DSMT4Equation.DSMT4（1）設(shè)EMBED Equation.DSMT4均成立，求EMBED Equation.DSMT4的取值范圍；（2）若EMBED Equation.DSMT4，證明：存在EM

6、BED Equation.DSMT4，使得Equation.DSMT4對(duì)EMBED Equation.DSMT4均成立， 并求EMBED Equation.DSMT4范圍（用EMBED Equation.DSMT4表示）10*（2017浙江）已知數(shù)列EMBED Equation.DSMT4，公差EMBED Equation.3的等比數(shù)列，EMBED的最小值是 _ ，為其前 項(xiàng)和， 若 成等比數(shù)列， 則 ， 其中EMBEDEquation.3成公比為Equation.3成公差為1的等差數(shù)列，則EMBED Equation.DSMT4的等差數(shù)列，公比為EMBED Equation.DSMT4，若E

7、MBED Equation.DSMT4EMBEDEMBED是首項(xiàng)為EMBED Equation.DSMT4，公差為EMBEDEquation.DSMT4是首項(xiàng) 為EMBED的等比數(shù)列對(duì)EMBED Equation.DSMT4滿足：EMBED Equation.DSMT4EMBED的取值(n)(m)*根據(jù)親所在地區(qū)選用，新課標(biāo)地區(qū)(文科)不考11(2017江蘇) 對(duì)于給定的正整數(shù)EMBED Equation.DSMT4滿足EMBED Equation.DSMT4對(duì)任意正整數(shù)EMBED Equation.DSMT4 EMBED Equation.DSMT4EMBED Equation.DSMT4是

8、“EMBED Equation.DSMT4數(shù)列”(1)證明：等差數(shù)列EMBED Equation.DSMT4是“EMBED Equation.DSMT4數(shù)列 ”；(2)若數(shù)列EMBED Equation.DSMT4既是“EMBED Equation.DSMT4數(shù)列 ”，又是“EMBED Equation.DSMT4數(shù)列 ”，證明：EMBED Equation.DSMT4是等差數(shù)列12(2016年四川)已知數(shù)列EMBED Equation.DSMT4的首項(xiàng)為1，EMBEDEquation.DSMT4為數(shù)列EMBED Equation.DSMT4的前EMBEDEquation.DSMT4項(xiàng)和，EM

9、BEDEquation.DSMT4，其中EMBEDEquation.DSMT4(I)若EMBED Equation.DSMT4成等差數(shù)列，求數(shù)列(n)設(shè)雙曲線EMBED Equation.DSMT4Equation.DSMT413(2016年浙江)(I)求通項(xiàng)公式 ；(II)求數(shù)列 的前14(2015重慶)已知等差數(shù)列EMBED Equation.DSMT43項(xiàng)和EMBED Equation.DSMT4(I) 求EMBED Equatio n.DSMT4的通項(xiàng)公式；(n)設(shè)等比數(shù)列EMBED Equatio n.DSMT4滿足Equation.DSMT4，求EMBED Equation.DSM

10、T4EMBED Equation.DSMT415(2015天津)已知EMBED Equation.DSMT4Equation.DSMT4是等差數(shù)列， 且EMBED Equation.DSMT4EMBED Equation.DSMT4(I) 求EMBED Equatio n.DSMT4禾 REMBED Equatio n.DSMT4的通項(xiàng)公式；( n ) 設(shè)EMBED Equation.DSMT4，EMBED Equation.DSMT4， 求數(shù) 列EMBEDEquatio n.DSMT4的前EMBED Equatio n.DSMT4項(xiàng)和.16(2015四川)設(shè)數(shù)列EMBED Equation.

11、DSMT4(EMBED Equation.DSMT4EMBED Equation.DSMT4項(xiàng)和EMBED Equation.DSMT4滿足EMBED Equation.DSMT4EMBED Equation.DSMT4，EMBED Equation.DSMT4 +1，EMBED Equation.DSMT4數(shù)列.(I)求數(shù)列EMBED Equatio n.DSMT4的通項(xiàng)公式；(n)設(shè)數(shù)歹列EMBED Equatio n.DSMT4的前EMBED Equatio n.DSMT4Equation.DSMT4，求EMBED Equation.DSMT4.17.(2015湖北)設(shè)等差數(shù)列EMBED

12、 Equation.DSMT4的公差為EMBED Equation.DSMT4， 前EMBEDEquation.DSMT4項(xiàng) 和 為EMBED Equation.DSMT4， 等比 數(shù)列EMBEDEquation.DSMT4的公比為EMBED Equation.DSMT4，已知EMBED Equation.DSMT4，EMBED Equation.DSMT4，EMBED Equation.DSMT4，EMBED Equation.DSMT4. (I)求數(shù)歹歹EMBEDEquatio n.DSMT4,EMBED Equatio n.DSMT4的通項(xiàng)公式；EMBEDEquation.DSMT4證明

13、：EMBED Equation.DSMT4EMBED Equation.DSMT4時(shí)EMBED Equation.DSMT4；EMBED Equation.DSMT4；EMBED Equation.DSMT4項(xiàng)和，EMBED Equation.DSMT4 EMBEDEquation.DSMT4 EMBEDEquation.DSMT4的通項(xiàng)公式；，且的離心率為 ，求EMBED Equation.DSMT4設(shè)數(shù)列 的前 項(xiàng)和為.已知=4，EMBED項(xiàng)和EMBED Equation.DSMT4前EMBED Equation.DSMT4是各項(xiàng)均為正數(shù)的等比數(shù)列，EMBED Equation.DSMT4

14、=1,2,3）的前，且 成等差，若數(shù)列EMBED Equation.DSMT4總成立，則稱(chēng)數(shù)列EMBED=2 +1，項(xiàng)和.滿足EMBED Equation.DSMT4，前EMBEDEMBED項(xiàng)和為( n ) 當(dāng)EMBED Equation.DSMT4時(shí)， 記EMBED Equation.DSMT4= EMBEDEquation.DSMT4，求數(shù)列EMBED Equation.DSMT4的前EMBED Equation.DSMT4項(xiàng) 和EMBED Equation.DSMT4.18. (2014山東) 已知等差數(shù)列EMBED Equation.KSEE3 * MERGEFORMAT的公差為2，前

15、EMBED Equation.DSMT4* MERGEFORMAT項(xiàng)和為EMBED Equation.KSEE3 * MERGEFORMAT，且EMBED Equation.KSEE3 * MERGEFORMAT，EMBED Equation.KSEE3 * MERGEFORMAT，EMBED Equation.KSEE3 * MERGEFORMAT成等比數(shù)列.(I)求數(shù)歹列EMBED Equati on .KSEE3 * MERGEFORMAT的通項(xiàng)公式；(n) 令EMBED Equatio n.KSEE3 * MERGEFORMAT= EMBED Equatio n.KSEE3 * MER

16、GEFORMAT求 數(shù) 列EMBED Equation.KSEE3 * MERGEFORMAT的 前EMBED Equation.DSMT4 * MERGEFORMAT項(xiàng)和EMBEDEquation.KSEE3 * MERGEFORMAT.19.(2014浙江)已知數(shù)列 和 滿足 .若 為等比數(shù)列，(I)求與；(n)設(shè).記數(shù)列的前項(xiàng)和為.(i)求；(ii) 求正整數(shù) ，使得對(duì)任意 ，均有.20.(2014湖南)已知數(shù)列 滿足(I)若 是遞增數(shù)列，且成等差數(shù)列，求 的值；(n)若，且 是遞增數(shù)列，是遞減數(shù)列，求數(shù)列21.(2014四川)設(shè)等差數(shù)列EMBED Equation.DSMT4點(diǎn)EMBE

17、D Equation.DSMT4在 函 數(shù)EMBED Equation.DSMT4).(I ) 若EMBED Equation.DSMT4Equation.DSMT4的圖象上， 求數(shù)列項(xiàng)和EMBED Equation.DSMT4(n) 若EMBED Equati on .DSMT4Equation.DSMT4處 的 切 線 在的通項(xiàng)公式.的公差為EMBED Equation.DSMT4Equation.DSMT4的 圖 象 上 (EMBED，點(diǎn)EMBED Equation.DSMT4 EMBEDEquation.DSMT4的前在 函 數(shù)EMBEDEMBED Equation.DSMT4的圖象在

18、點(diǎn) 軸 上的 截距 為Equation.DSMT4，求數(shù)列EMBED Equation.DSMT4和EMBEDEquation.DSMT4.22. (2014江蘇)設(shè)數(shù)列 的前 項(xiàng)和為 .若對(duì)任意正整數(shù) 列”.，函數(shù)EMBED Equation.DSMT4EMBED Equation.DSMT4的前EMBED Equation.DSMT4EMBEDEMBED項(xiàng)，總存在正整數(shù) ，使得 ，則稱(chēng) 是 “H數(shù)若數(shù)列 的前n項(xiàng)和( N設(shè) 是等差數(shù)列，其首項(xiàng) 證明：對(duì)任意的等差數(shù)列(n)(皿)23(2013安徽)設(shè)數(shù)列 滿足(I)求數(shù)列 的通項(xiàng)公式；(n)若，求數(shù)列的前項(xiàng)和24(2013廣東)設(shè)各項(xiàng)均為正

19、數(shù)的數(shù)列 且 構(gòu)成等比數(shù)列(I)證明：；(n)求數(shù)列 的通項(xiàng)公式；(皿)證明：對(duì)一切正整數(shù) ，有.25(2013湖北)已知 是等比數(shù)列 的前 且.(I)求數(shù)列 的通項(xiàng)公式；(n)是否存在正整數(shù) 若不存在，說(shuō)明理由.26.(2013江蘇)設(shè)(I) 若 ，且 ，),證明：是H數(shù)列”，公差 若，總存在兩個(gè)， ，且對(duì)任意是H數(shù)列”求的值;H數(shù)列 ”，函數(shù)和 ，使得( N )成立 ，滿足的前項(xiàng)和，項(xiàng)和為，滿足成等差數(shù)列，使得 ？若存在，是首項(xiàng)為 ，公差為成等比數(shù)列，證明：求出符合條件的所有 的集合;的等差數(shù)列是其前 項(xiàng)和.記 ， ，其中 為實(shí)數(shù).(n) 若 是等差數(shù)列，證明： .27.(2012山東)已

20、知等差數(shù)列 的前5項(xiàng)和為105，且 .(I)求數(shù)列 的通項(xiàng)公式；(n)對(duì)任意 ，將數(shù)列 中不大于 的項(xiàng)的個(gè)數(shù)記為.求數(shù)列 的前m項(xiàng)和.28(2012湖南)某公司一下屬企業(yè)從事某種高科技產(chǎn)品的生產(chǎn)該企業(yè)第一年年初有資金 萬(wàn)元，將其投入生產(chǎn)， 到當(dāng)年年底資金增長(zhǎng)了50 .預(yù)計(jì)以后每年資金年增長(zhǎng)率與第一年的相同.司要求企業(yè)從第一年開(kāi)始， 每年年底上繳資金EMBED Equation.DSMT4投入下一年生產(chǎn).設(shè)第EMBED Equation.DSMT4年年底企業(yè)上繳資金后的剩余資金為Equation.DSMT4萬(wàn)元.(I)用EMBED Equatio n.DSMT4表示EMBED Equatio n

21、.DSMT4Equation.DSMT4的關(guān)系式；(n)若公司希望經(jīng)過(guò)EMBED Equatio n.DSMT4剩余資金為4000萬(wàn)元，試確定企業(yè)每年上繳資金Equation.DSMT4表示).2000公 萬(wàn)元， 并將剩余資金全部EMBED，并寫(xiě)出與EMBED(EMBED Equati on .DSMT4紹)EMBED Equation.DSMT4的值(用年使企業(yè)的EMBED29.(2012浙江)已知數(shù)列EMBEDEquation.DSMT4的前EMBED Equation.DSMT4，且EMBED Equation.DSMT4 =列EMBEDEquation.DSMT4滿足EMBED Equ

22、ation.DSMT4(I) 求EMBED Equatio n.DSMT4；( n ) 求 數(shù) 列EMBED Equation.DSMT4Equation.DSMT4.30.(2012山東)在等差數(shù)列中， ，(I)求數(shù)列 的通項(xiàng)公式；(n)對(duì)任意的 ，將數(shù)列 中落入?yún)^(qū)間 內(nèi)的項(xiàng)的個(gè)數(shù)為31.(2012江蘇)已知 各項(xiàng)均為正數(shù)的兩個(gè)數(shù)列Equation.DSMT4滿足：EMBED Equation.DSMT4(I)設(shè)EMBED Equatio n.DSMT4，求證：數(shù)列EMBED Equation.DSMT4EMBED Equation.DSMT4，EMBED Equation.DSMT4項(xiàng)和為

23、，數(shù)的前EMBED Equation.DSMT4，求數(shù)列 的前 項(xiàng)和 EMBED Equation.DSMT4EMBED Equation.DSMT4項(xiàng)和EMBEDEMBED是等差數(shù)列； 是等比數(shù)列，求EMBED(n)設(shè)EMBED Equation.DSMT4, 且EMBED Equation.DSMT4Equation.DSMT4和EMBED Equation.DSMT4的值.32.(2011天津)已知數(shù)列EMBED Equation.DSMT4滿足EMBEDEquation.DSMT4 EMBED Equation.DSMT4.(I)求(n)設(shè)(m )設(shè)EMBED Equation.DSMT4EMBED Equation.DSMT4EMBED Equation.DSMT4EMBED Equation.DSMT4的值；，證明EMBED Equation.DSMT4Equation.DSMT4為EMBED是等比數(shù)列；的 前EMBEDEquation.DSMT4項(xiàng)和，證明33.(2011天津)已知數(shù)列EMBED Equation.DSMT4(l)求EMBED Equatio n.DSMT4(n)設(shè)EMBED Equati on .DSMT4(