2024届全国各地高考押题数学(理科)精选试题分类汇编5：数列2.doc

文档介绍：该【2024届全国各地高考押题数学(理科)精选试题分类汇编5：数列2 】是由【朱老师】上传分享，文档一共【21】页，该文档可以免费在线阅读，需要了解更多关于【2024届全国各地高考押题数学(理科)精选试题分类汇编5：数列2 】的内容，可以使用淘豆网的站内搜索功能，选择自己适合的文档，以下文字是截取该文章内的部分文字，如需要获得完整电子版，请下载此文档到您的设备，方便您编辑和打印。ofruraldrinkingwatersources,pletewithwarningsigns,workprotectionfacilitiesofruraldrinkingwatersources,pletewithwarningsigns,workprotectionfacilitiesofruraldrinkingwatersources,pletewithwarningsigns,workprotectionfacilities2024届全国各地高考押题数学〔理科〕精选试题分类汇编5:数列一、选择题.〔2024届北京市高考压轴卷理科数学〕为等差数列,为其前项和,那么 〔〕A. B. C. D.【答案】A【解析】设公差为,那么由得,即,解得,所以,,选 〔〕A..〔2024届天津市高考压轴卷理科数学〕设是公差不为0的等差数列的前项和,且成等比数列,那么等于 〔〕 【答案】C【解析】因为成等比数列,所以,即,即,所以,选 C..〔2024届浙江省高考压轴卷数学理试题〕数列的前项和满足:,且,那么 〔〕 【答案】A[来源:Z#xx#]【解析】,可得,,可得,同理可得,应选 〔〕A..〔2024届全国大纲版高考压轴卷数学理试题〕等比数列中,公比假设那么有 〔〕-4 -4 【答案】 =号ofruraldrinkingwatersources,pletewithwarningsigns,workprotectionfacilitiesofruraldrinkingwatersources,pletewithwarningsigns,workprotectionfacilitiesofruraldrinkingwatersources,pletewithwarningsigns,workprotectionfacilities.〔2024届四川省高考压轴卷数学理试题〕假设等比数列满足,,那么的值是 〔〕A. B. 【答案】C.〔2024届福建省高考压轴卷数学理试题〕设等差数列的前项和是,假设(N*,且),那么必定有 〔〕A.,且 B.,且C.,且 D.,且【答案】C【解析】由题意,得:.显然,易得,.〔2024届全国大纲版高考压轴卷数学理试题〕数列的通项公式为,那么满足的整数 〔〕 【答案】 ,检验,时,,,,满足题意由对称性知,.所以,均满足题.〔2024届辽宁省高考压轴卷数学理试题〕是首项为1的等比数列,是的前n项和,且,那么数列ofruraldrinkingwatersources,pletewithwarningsigns,workprotectionfacilitiesofruraldrinkingwatersources,pletewithwarningsigns,workprotectionfacilitiesofruraldrinkingwatersources,pletewithwarningsigns,workprotectionfacilities的前5项和为 〔〕 C. D.【答案】C【解析】此题主要考查等比数列前n项和公式及等比数列的性质,,所以,所以是首项为1,公比为的等比数列,前5项和..〔2024届湖南省高考压轴卷数学〔理〕试题〕等比数列中,各项都是正数,且成等差数列,那么等于【全,品中&高*考*网】 〔〕A. B. C. D.【答案】C.〔2024届重庆省高考压轴卷数学理试题〕设正数满足,那么 〔〕A. B. C. D.【答案】B.〔2024届福建省高考压轴卷数学理试题〕设等差数列满足:,,数列的前项和取得最大值,那么首项的取值范围是 〔〕A. B. C. D.【答案】B【解析】先化简:ofruraldrinkingwatersources,pletewithwarningsigns,workprotectionfacilitiesofruraldrinkingwatersources,pletewithwarningsigns,workprotectionfacilitiesofruraldrinkingwatersources,pletewithwarningsigns,workprotectionfacilities又当且仅当时,数列的前项和取得最大值,即:二、填空题.〔2024届浙江省高考压轴卷数学理试题〕,假设(a,t均为正实数),那么类比以上等式,可推测a,t的值,a+t=_______.【答案】41【解析】照此规律:a=6,t=a2-1=35.〔2024届上海市高考压轴卷数学〔理〕试题〕数列是等差数列,数列是等比数列,那么的值为_____________.【答案】【解析】因为是等差数列,所以是等比数列,所以,因为,所以,所以.[来源:学科网].〔2024届浙江省高考压轴卷数学理试题〕数列{an}满足a1=1,an+1=an+2n,那么a10=____________.[来源:Z|xx|]【答案】1023【解析】累加法..〔2024届广东省高考压轴卷数学理试题〕定义映射,其中,,对所有的有序正整数对满足下述条件:①;②假设,;③,那么___,,pletewithwarningsigns,workprotectionfacilitiesofruraldrinkingwatersources,pletewithwarningsigns,workprotectionfacilitiesofruraldrinkingwatersources,pletewithwarningsigns,workprotectionfacilities【答案】解:根据定义得.,,,所以根据归纳推理可知..〔2024届陕西省高考压轴卷数学〔理〕试题〕“公差为的等差数列数列的前项的和为,那么数列是公差为的等差数列〞,类比上述性质有:“公比为的等比数列数列的前项的和为,那么数列___________________________〞.【答案】是公比为的等比数列【解析】,∴是公比为的等比数列.[来源:.].〔2024届安徽省高考压轴卷数学理试题〕设等差数列的公差,且,当时,的前项和取得最小值,那么的取值范围是__________.【答案】【解析】,是前项和取得最小值,解得..〔2024届江苏省高考压轴卷数学试题〕在如图的表格中,每格填上一个数字后,使得每一横行成等差数列,每一纵列成等比数列,,pletewithwarningsigns,workprotectionfacilitiesofruraldrinkingwatersources,pletewithwarningsigns,workprotectionfacilitiesofruraldrinkingwatersources,pletewithwarningsigns,workprotectionfacilitiesbc【答案】1 .〔2024届福建省高考压轴卷数学理试题〕无穷数列的首项是,随后两项都是,接下来项都是,再接下来项都是,,,假设,,那么________.【答案】【解析】,第组有个数,以此类推...显然在第组,,,..〔2024届江西省高考压轴卷数学理试题〕是一个公差大于0的等差数列,,记数列的前项和为,对任意的,不等式恒成立,那么实数的最小值是_______.【答案】100三、解答题.〔2024届新课标高考压轴卷〔二〕理科数学〕数列的首项为,前n项和为,且(Ⅰ)证明数列是等比数列(Ⅱ)令,求函数在点处的导数,并比较与的大小.【答案】(1)解:(1),(2)两列相减得当时,,故总有,,又,ofruraldrinkingwatersources,pletewithwarningsigns,workprotectionfacilitiesofruraldrinkingwatersources,pletewithwarningsigns,workprotectionfacilitiesofruraldrinkingwatersources,pletewithwarningsigns,workprotectionfacilities从而,即数列是等比数列由(1)知==(1)当n=1时(1)式为0当n=2时(1)式为-12当时,又即(1)式>0.〔2024新课标高考压轴卷〔一〕理科数学〕在等差数列中,,其前项和为,等比数列的各项均为正数,,公比为,且,.(1)求与;(2)设数列满足,求的前项和.【答案】解:(1),pletewithwarningsigns,workprotectionfacilitiesofruraldrinkingwatersources,pletewithwarningsigns,workprotectionfacilitiesofruraldrinkingwatersources,pletewithwarningsigns,workprotectionfacilities解得或(舍),.故,.(2)由(1)可知,,..〔2024届山东省高考压轴卷理科数学〕设数列的前项积为,且.(Ⅰ)求证数列是等差数列;(Ⅱ)设,求数列的前项和.【答案】【解析】(Ⅰ)由题意可得:,所以(Ⅱ)数列为等差数列,,,,.〔2024届湖北省高考压轴卷数学〔理〕试题〕等比数列满足:,且是的等差中项.(1)求数列的通项公式;(2)假设,,求使成立的正整数的最小值.【答案】(1)设等比数列的首项为,公比为,ofruraldrinkingwatersources,pletewithwarningsigns,workprotectionfacilitiesofruraldrinkingwatersources,pletewithwarningsigns,workprotectionfacilitiesofruraldrinkingwatersources,pletewithwarningsigns,workprotectionfacilities依题意,有由①及,,②式不成立;当时,②得,所以.(2),∴,③.④③-④,得,,;当时,.故使成立的正整数的最小值为5..〔2024届江苏省高考压轴卷数学试题〕等差数列{an},且对任意正整数n都有.(1)求数列{an}的通项公式及Sn;(2)是否存在正整数n和k,使得Sn,Sn+1,Sn+k成等比数列?假设存在,求出n和k的值;假设不存在,请说明理由.【答案】ofruraldrinkingwatersources,pletewithwarningsigns,workprotectionfacilitiesofruraldrinkingwatersources,pletewithwarningsigns,workprotectionfacilitiesofruraldrinkingwatersources,pletewithwarningsigns,workprotectionfacilities.〔2024届北京市高考压轴卷理科数学〕数列是等差数列,是等比数列,且,,.(1)求数列和的通项公式(2)数列满足,求数列的前项和.【答案】(Ⅰ)设的公差为,的公比为由,得,从而[来源:学,科,网Z,X,X,K]因此又,从而,故(Ⅱ)令两式相减得