新高考數(shù)學(xué)二輪復(fù)習(xí)核心考點(diǎn)講與練重難點(diǎn)06兩種數(shù)列最值求法原卷版

重難點(diǎn)06兩種數(shù)列最值求法（核心考點(diǎn)講與練）題型一：?jiǎn)握{(diào)性法求數(shù)列最值一、單選題1．（2022·安徽淮南·二模（文））已知等差數(shù)列SKIPIF1<0的前n項(xiàng)和為SKIPIF1<0，SKIPIF1<0，則數(shù)列SKIPIF1<0（

）A．有最大項(xiàng)，無(wú)最小項(xiàng) B．有最小項(xiàng)，無(wú)最大項(xiàng)C．既無(wú)最大項(xiàng)，又無(wú)最小項(xiàng) D．既有最大項(xiàng)，又有最小項(xiàng)2．（2022·北京·二模）已知等差數(shù)列SKIPIF1<0與等比數(shù)列SKIPIF1<0的首項(xiàng)均為－3，且SKIPIF1<0，SKIPIF1<0，則數(shù)列SKIPIF1<0（

）A．有最大項(xiàng)，有最小項(xiàng) B．有最大項(xiàng)，無(wú)最小項(xiàng)C．無(wú)最大項(xiàng)，有最小項(xiàng) D．無(wú)最大項(xiàng)，無(wú)最小項(xiàng)3．（2022·安徽·蕪湖一中三模（文））已知等差數(shù)列SKIPIF1<0的首項(xiàng)SKIPIF1<0，且SKIPIF1<0，正項(xiàng)等比數(shù)列SKIPIF1<0的首項(xiàng)SKIPIF1<0，且SKIPIF1<0，若數(shù)列SKIPIF1<0的前n項(xiàng)和為SKIPIF1<0，則數(shù)列SKIPIF1<0的最大項(xiàng)的值為（

）A．SKIPIF1<0 B．1 C．SKIPIF1<0 D．24．（2022·廣東·一模）已知正項(xiàng)數(shù)列SKIPIF1<0滿足SKIPIF1<0，當(dāng)SKIPIF1<0最大時(shí)，SKIPIF1<0的值為（

）A．2 B．3 C．4 D．5二、多選題5．（2021·廣東·高三階段練習(xí)）設(shè)數(shù)列SKIPIF1<0的前n項(xiàng)和為SKIPIF1<0，若SKIPIF1<0，則下列結(jié)論中正確的是（

）A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．滿足SKIPIF1<0的n的最大值為20206．（2022·全國(guó)·高三專(zhuān)題練習(xí)）等比數(shù)列SKIPIF1<0各項(xiàng)均為正數(shù)，SKIPIF1<0，SKIPIF1<0，數(shù)列SKIPIF1<0的前SKIPIF1<0項(xiàng)積為SKIPIF1<0，則（

）A．?dāng)?shù)列SKIPIF1<0單調(diào)遞增 B．?dāng)?shù)列SKIPIF1<0單調(diào)遞減C．當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0最大 D．當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0最小7．（2021·河北·高三階段練習(xí)）已知SKIPIF1<0，SKIPIF1<0分別是等差數(shù)列SKIPIF1<0的公差及前SKIPIF1<0項(xiàng)和，SKIPIF1<0，設(shè)SKIPIF1<0，數(shù)列SKIPIF1<0的前SKIPIF1<0項(xiàng)和為SKIPIF1<0，則下列結(jié)論中正確的是（

）A．滿足SKIPIF1<0的最小SKIPIF1<0值為SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0時(shí)，SKIPIF1<0取得最小值8．（2022·江蘇·高三專(zhuān)題練習(xí)）在SKIPIF1<0（SKIPIF1<0）中，內(nèi)角SKIPIF1<0的對(duì)邊分別為SKIPIF1<0，SKIPIF1<0的面積為SKIPIF1<0，若SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0，SKIPIF1<0，則（

）A．SKIPIF1<0一定是直角三角形 B．SKIPIF1<0為遞增數(shù)列C．SKIPIF1<0有最大值 D．SKIPIF1<0有最小值9．（2021·江蘇·鹽城中學(xué)一模）對(duì)于數(shù)列SKIPIF1<0，若存在數(shù)列SKIPIF1<0滿足SKIPIF1<0（SKIPIF1<0），則稱(chēng)數(shù)列SKIPIF1<0是SKIPIF1<0的“倒差數(shù)列”，下列關(guān)于“倒差數(shù)列”描述正確的是（

）A．若數(shù)列SKIPIF1<0是單增數(shù)列，但其“倒差數(shù)列”不一定是單增數(shù)列；B．若SKIPIF1<0，則其“倒差數(shù)列”有最大值；C．若SKIPIF1<0，則其“倒差數(shù)列”有最小值；D．若SKIPIF1<0，則其“倒差數(shù)列”有最大值.三、填空題10．（2022·上海徐匯·二模）已知定義在SKIPIF1<0上的函數(shù)SKIPIF1<0滿足SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0．設(shè)SKIPIF1<0在區(qū)間SKIPIF1<0上的最小值為SKIPIF1<0．若存在SKIPIF1<0，使得SKIPIF1<0有解，則實(shí)數(shù)SKIPIF1<0的取值范圍是______________．11．（2022·浙江臺(tái)州·二模）已知等差數(shù)列SKIPIF1<0的各項(xiàng)均為正數(shù)，且數(shù)列SKIPIF1<0的前SKIPIF1<0項(xiàng)和為SKIPIF1<0，則數(shù)列SKIPIF1<0的最大項(xiàng)為_(kāi)__________.（用數(shù)字作答）12．（2022·全國(guó)·高三專(zhuān)題練習(xí)）已知數(shù)列{an}對(duì)任意m，n∈N*都滿足am+n=am+an，且a1=1，若命題“?n∈N*，λan≤SKIPIF1<0+12”為真，則實(shí)數(shù)λ的最大值為_(kāi)___.13．（2022·天津市新華中學(xué)高三期末）在數(shù)列SKIPIF1<0中，SKIPIF1<0，則數(shù)列SKIPIF1<0中的最大項(xiàng)的SKIPIF1<0________.14．（2022·全國(guó)·高三專(zhuān)題練習(xí)）已知等比數(shù)列{an}的前n項(xiàng)和為Sn，若a1＝SKIPIF1<0，an＋2an＋1＝0，則Sn－SKIPIF1<0的最大值與最小值的積為_(kāi)_______.15．（2022·河南·模擬預(yù)測(cè)（文））已知數(shù)列SKIPIF1<0滿足SKIPIF1<0，則SKIPIF1<0的最大值為_(kāi)_______．16．（2022·全國(guó)·模擬預(yù)測(cè)）已知數(shù)列SKIPIF1<0的前n項(xiàng)和為SKIPIF1<0，等差數(shù)列SKIPIF1<0的首項(xiàng)為1，公差為1，則SKIPIF1<0的最大值為_(kāi)_________.四、解答題17．（2022·湖北·模擬預(yù)測(cè)）已知數(shù)列SKIPIF1<0的前n項(xiàng)之積為SKIPIF1<0，且SKIPIF1<0．(1)求數(shù)列SKIPIF1<0和SKIPIF1<0的通項(xiàng)公式；(2)求SKIPIF1<0的最大值．18．（2022·天津市寧河區(qū)蘆臺(tái)第一中學(xué)模擬預(yù)測(cè)）設(shè)數(shù)列SKIPIF1<0的前SKIPIF1<0項(xiàng)和為SKIPIF1<0,且滿足SKIPIF1<0.(1)求數(shù)列SKIPIF1<0的通項(xiàng)公式;(2)記SKIPIF1<0，數(shù)列SKIPIF1<0的前SKIPIF1<0項(xiàng)和為SKIPIF1<0，若不等式SKIPIF1<0對(duì)一切SKIPIF1<0恒成立,求SKIPIF1<0的取值范圍.19．（2022·天津·高三專(zhuān)題練習(xí)）設(shè)數(shù)列SKIPIF1<0的前SKIPIF1<0項(xiàng)和SKIPIF1<0．(1)求數(shù)列SKIPIF1<0的通項(xiàng)公式；(2)若SKIPIF1<0求SKIPIF1<0的前SKIPIF1<0項(xiàng)和SKIPIF1<0取最小值時(shí)SKIPIF1<0的值；(3)證明：SKIPIF1<020．（2022·重慶巴蜀中學(xué)高三階段練習(xí)）已知數(shù)列SKIPIF1<0的首項(xiàng)SKIPIF1<0，SKIPIF1<0.(1)證明：數(shù)列SKIPIF1<0是等比數(shù)列；(2)求數(shù)列SKIPIF1<0的前SKIPIF1<0項(xiàng)和SKIPIF1<0的最小值.21．（2022·遼寧實(shí)驗(yàn)中學(xué)模擬預(yù)測(cè)）已知數(shù)列SKIPIF1<0的前n項(xiàng)和為SKIPIF1<0，滿足：SKIPIF1<0(1)求證：數(shù)列SKIPIF1<0為等差數(shù)列；(2)若SKIPIF1<0，令SKIPIF1<0，數(shù)列SKIPIF1<0的前n項(xiàng)和為SKIPIF1<0，若不等式SKIPIF1<0對(duì)任意SKIPIF1<0恒成立，求實(shí)數(shù)m的取值范圍．題型二：不等法求數(shù)列最值一、單選題1．（2022·河南·高三階段練習(xí)（理））已知曲線SKIPIF1<0在點(diǎn)SKIPIF1<0處的切線為l，數(shù)列SKIPIF1<0的首項(xiàng)為1，點(diǎn)SKIPIF1<0為切線l上一點(diǎn)，則數(shù)列SKIPIF1<0中的最小項(xiàng)為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2021·遼寧·建平縣實(shí)驗(yàn)中學(xué)高三階段練習(xí)）已知數(shù)列SKIPIF1<0滿足SKIPIF1<0，SKIPIF1<0，若SKIPIF1<0，且存在SKIPIF1<0，使得SKIPIF1<0成立，則實(shí)數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．（2021·浙江·高三期中）已知數(shù)列SKIPIF1<0滿足SKIPIF1<0，SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2020·江西·鷹潭一中高三期中（文））數(shù)列SKIPIF1<0通項(xiàng)公式為：SKIPIF1<0，則SKIPIF1<0中的最大項(xiàng)為（

）A．第1項(xiàng) B．第1010項(xiàng) C．第1011項(xiàng) D．第1012項(xiàng)二、多選題5．（2022·全國(guó)·高三專(zhuān)題練習(xí)）在數(shù)列{an}中，an＝(n＋1)SKIPIF1<0n，則數(shù)列{an}中的最大項(xiàng)可以是（

）A．第6項(xiàng) B．第7項(xiàng)C．第8項(xiàng) D．第9項(xiàng)6．（2022·全國(guó)·高三專(zhuān)題練習(xí)）已知數(shù)列SKIPIF1<0滿足SKIPIF1<0，下列命題正確的有（

）A．當(dāng)SKIPIF1<0時(shí)，數(shù)列SKIPIF1<0為遞減數(shù)列B．當(dāng)SKIPIF1<0時(shí)，數(shù)列SKIPIF1<0一定有最大項(xiàng)C．當(dāng)SKIPIF1<0時(shí)，數(shù)列SKIPIF1<0為遞減數(shù)列D．當(dāng)SKIPIF1<0為正整數(shù)時(shí)，數(shù)列SKIPIF1<0必有兩項(xiàng)相等的最大項(xiàng)7．（2020·河北·滄州市民族中學(xué)高三階段練習(xí)）已知數(shù)列SKIPIF1<0的前SKIPIF1<0項(xiàng)和為SKIPIF1<0，且SKIPIF1<0，SKIPIF1<0，著不等式SKIPIF1<0對(duì)任意的SKIPIF1<0恒成立，則下列結(jié)論正確的為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0的最大值為SKIPIF1<0 D．SKIPIF1<0的最小值為SKIPIF1<0三、填空題8．（2022·安徽亳州·高三期末（理））已知數(shù)列SKIPIF1<0滿足SKIPIF1<0，SKIPIF1<0，若不等式SKIPIF1<0對(duì)任意SKIPIF1<0恒成立，則實(shí)數(shù)SKIPIF1<0的取值范圍是___________.9．（2021·湖北·高三階段練習(xí)）已知數(shù)列SKIPIF1<0的首項(xiàng)SKIPIF1<0，其前SKIPIF1<0項(xiàng)和為SKIPIF1<0，且滿足SKIPIF1<0，則當(dāng)SKIPIF1<0取得最小值時(shí)，SKIPIF1<0___________.四、解答題10．（2022·全國(guó)·模擬預(yù)測(cè)（理））已知數(shù)列SKIPIF1<0滿足SKIPIF1<0，且SKIPIF1<0．(1)求數(shù)列SKIPIF1<0的通項(xiàng)公式；(2)設(shè)SKIPIF1<0，且數(shù)列SKIPIF1<0的前n項(xiàng)和為SKIPIF1<0，若SKIPIF1<0恒成立，求SKIPIF1<0的取值范圍．11．（2022·全國(guó)·高三專(zhuān)題練習(xí)）數(shù)列SKIPIF1<0滿足SKIPIF1<0，(1)求SKIPIF1<0的值；(2)求數(shù)列SKIPIF1<0前SKIPIF1<0項(xiàng)和SKIPIF1<0；(3)令SKIPIF1<0，SKIPIF1<0，證明：數(shù)列SKIPIF1<0的前SKIPIF1<0項(xiàng)和SKIPIF1<0滿足SKIPIF1<0．12．（2022·全國(guó)·高三專(zhuān)題練習(xí)（文））已知數(shù)列SKIPIF1<0是遞增的等比數(shù)列，且SKIPIF1<0，SKIPIF1<0．(1)求數(shù)列SKIPIF1<0的通項(xiàng)公式；(2)記數(shù)列SKIPIF1<0的前SKIPIF1<0項(xiàng)和為SKIPIF1<0，求使SKIPIF1<0成立的正整數(shù)SKIPIF1<0的最小值．13．（2022·全國(guó)·高三專(zhuān)題練習(xí)）已知數(shù)列SKIPIF1<0的各項(xiàng)均為正數(shù)，前SKIPIF1<0項(xiàng)和為SKIPIF1<0，SKIPIF1<0.（