新高考數(shù)學二輪復習核心考點講與練重難點06兩種數(shù)列最值求法原卷版

重難點06兩種數(shù)列最值求法（核心考點講與練）題型一：單調(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項和為SKIPIF1<0，SKIPIF1<0，則數(shù)列SKIPIF1<0（

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

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

）A．SKIPIF1<0 B．1 C．SKIPIF1<0 D．24．（2022·廣東·一模）已知正項數(shù)列SKIPIF1<0滿足SKIPIF1<0，當SKIPIF1<0最大時，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）設數(shù)列SKIPIF1<0的前n項和為SKIPIF1<0，若SKIPIF1<0，則下列結論中正確的是（

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

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

）A．滿足SKIPIF1<0的最小SKIPIF1<0值為SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0時，SKIPIF1<0取得最小值8．（2022·江蘇·高三專題練習）在SKIPIF1<0（SKIPIF1<0）中，內(nèi)角SKIPIF1<0的對邊分別為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·鹽城中學一模）對于數(shù)列SKIPIF1<0，若存在數(shù)列SKIPIF1<0滿足SKIPIF1<0（SKIPIF1<0），則稱數(shù)列SKIPIF1<0是SKIPIF1<0的“倒差數(shù)列”，下列關于“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SKIPIF1<0時，SKIPIF1<0．設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，則實數(shù)SKIPIF1<0的取值范圍是______________．11．（2022·浙江臺州·二模）已知等差數(shù)列SKIPIF1<0的各項均為正數(shù)，且數(shù)列SKIPIF1<0的前SKIPIF1<0項和為SKIPIF1<0，則數(shù)列SKIPIF1<0的最大項為___________.（用數(shù)字作答）12．（2022·全國·高三專題練習）已知數(shù)列{an}對任意m，n∈N*都滿足am+n=am+an，且a1=1，若命題“?n∈N*，λan≤SKIPIF1<0+12”為真，則實數(shù)λ的最大值為____.13．（2022·天津市新華中學高三期末）在數(shù)列SKIPIF1<0中，SKIPIF1<0，則數(shù)列SKIPIF1<0中的最大項的SKIPIF1<0________.14．（2022·全國·高三專題練習）已知等比數(shù)列{an}的前n項和為Sn，若a1＝SKIPIF1<0，an＋2an＋1＝0，則Sn－SKIPIF1<0的最大值與最小值的積為________.15．（2022·河南·模擬預測（文））已知數(shù)列SKIPIF1<0滿足SKIPIF1<0，則SKIPIF1<0的最大值為________．16．（2022·全國·模擬預測）已知數(shù)列SKIPIF1<0的前n項和為SKIPIF1<0，等差數(shù)列SKIPIF1<0的首項為1，公差為1，則SKIPIF1<0的最大值為__________.四、解答題17．（2022·湖北·模擬預測）已知數(shù)列SKIPIF1<0的前n項之積為SKIPIF1<0，且SKIPIF1<0．(1)求數(shù)列SKIPIF1<0和SKIPIF1<0的通項公式；(2)求SKIPIF1<0的最大值．18．（2022·天津市寧河區(qū)蘆臺第一中學模擬預測）設數(shù)列SKIPIF1<0的前SKIPIF1<0項和為SKIPIF1<0,且滿足SKIPIF1<0.(1)求數(shù)列SKIPIF1<0的通項公式;(2)記SKIPIF1<0，數(shù)列SKIPIF1<0的前SKIPIF1<0項和為SKIPIF1<0，若不等式SKIPIF1<0對一切SKIPIF1<0恒成立,求SKIPIF1<0的取值范圍.19．（2022·天津·高三專題練習）設數(shù)列SKIPIF1<0的前SKIPIF1<0項和SKIPIF1<0．(1)求數(shù)列SKIPIF1<0的通項公式；(2)若SKIPIF1<0求SKIPIF1<0的前SKIPIF1<0項和SKIPIF1<0取最小值時SKIPIF1<0的值；(3)證明：SKIPIF1<020．（2022·重慶巴蜀中學高三階段練習）已知數(shù)列SKIPIF1<0的首項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項和SKIPIF1<0的最小值.21．（2022·遼寧實驗中學模擬預測）已知數(shù)列SKIPIF1<0的前n項和為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項和為SKIPIF1<0，若不等式SKIPIF1<0對任意SKIPIF1<0恒成立，求實數(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（理））已知曲線SKIPIF1<0在點SKIPIF1<0處的切線為l，數(shù)列SKIPIF1<0的首項為1，點SKIPIF1<0為切線l上一點，則數(shù)列SKIPIF1<0中的最小項為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2021·遼寧·建平縣實驗中學高三階段練習）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通項公式為：SKIPIF1<0，則SKIPIF1<0中的最大項為（

）A．第1項 B．第1010項 C．第1011項 D．第1012項二、多選題5．（2022·全國·高三專題練習）在數(shù)列{an}中，an＝(n＋1)SKIPIF1<0n，則數(shù)列{an}中的最大項可以是（

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

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

）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對任意SKIPIF1<0恒成立，則實數(shù)SKIPIF1<0的取值范圍是___________.9．（2021·湖北·高三階段練習）已知數(shù)列SKIPIF1<0的首項SKIPIF1<0，其前SKIPIF1<0項和為SKIPIF1<0，且滿足SKIPIF1<0，則當SKIPIF1<0取得最小值時，SKIPIF1<0___________.四、解答題10．（2022·全國·模擬預測（理））已知數(shù)列SKIPIF1<0滿足SKIPIF1<0，且SKIPIF1<0．(1)求數(shù)列SKIPIF1<0的通項公式；(2)設SKIPIF1<0，且數(shù)列SKIPIF1<0的前n項和為SKIPIF1<0，若SKIPIF1<0恒成立，求SKIPIF1<0的取值范圍．11．（2022·全國·高三專題練習）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項和SKIPIF1<0；(3)令SKIPIF1<0，SKIPIF1<0，證明：數(shù)列SKIPIF1<0的前SKIPIF1<0項和SKIPIF1<0滿足SKIPIF1<0．12．（2022·全國·高三專題練習（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的通項公式；(2)記數(shù)列SKIPIF1<0的前SKIPIF1<0項和為SKIPIF1<0，求使SKIPIF1<0成立的正整數(shù)SKIPIF1<0的最小值．13．（2022·全國·高三專題練習）已知數(shù)列SKIPIF1<0的各項均為正數(shù)，前SKIPIF1<0項和為SKIPIF1<0，SKIPIF1<0.（