新高考數(shù)學(xué)二輪復(fù)習(xí)強(qiáng)化練習(xí)專題12 數(shù)列的基本運(yùn)算（練）（原卷版）

第一篇熱點(diǎn)、難點(diǎn)突破篇專題12數(shù)列的基本運(yùn)算（練）【對(duì)點(diǎn)演練】一、單選題1．（2022春·江蘇南京·高三期末）若等差數(shù)列SKIPIF1<0的前5項(xiàng)和為75，SKIPIF1<0，則SKIPIF1<0（

）A．40 B．45 C．50 D．552．（2022春·江蘇·高三江蘇省新海高級(jí)中學(xué)校聯(lián)考階段練習(xí)）已知等比數(shù)列SKIPIF1<0的各項(xiàng)均為正數(shù)，它的前SKIPIF1<0項(xiàng)和為SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0（

）A．27 B．64 C．81 D．1283．（2023·廣西桂林·統(tǒng)考一模）已知正項(xiàng)等比數(shù)列SKIPIF1<0}滿足SKIPIF1<0為SKIPIF1<0與SKIPIF1<0的等比中項(xiàng)，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．24．（2022春·北京大興·高三統(tǒng)考期末）已知數(shù)列SKIPIF1<0中，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則下列結(jié)論錯(cuò)誤的是（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0是等比數(shù)列 D．SKIPIF1<0二、多選題5．（2022春·黑龍江佳木斯·高三佳木斯一中?？计谥校┮阎獢?shù)列SKIPIF1<0為等差數(shù)列，其前n項(xiàng)和為SKIPIF1<0，且SKIPIF1<0，SKIPIF1<0，則下列結(jié)論正確的是（

）A．SKIPIF1<0 B．公差SKIPIF1<0C．當(dāng)SKIPIF1<0時(shí)SKIPIF1<0最大 D．使SKIPIF1<0的n的最大值為166．（2022春·江蘇南通·高三海安高級(jí)中學(xué)期中）設(shè)SKIPIF1<0是公差為d的等差數(shù)列，SKIPIF1<0是其前n項(xiàng)的和，且SKIPIF1<0，SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0三、填空題7．（2023·廣西桂林·統(tǒng)考一模）記SKIPIF1<0為等差數(shù)列SKIPIF1<0的前n項(xiàng)和.若SKIPIF1<0，則SKIPIF1<0=___________.8．（2022·全國(guó)·高三專題練習(xí)）已知數(shù)列SKIPIF1<0中，SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0SKIPIF1<0，則SKIPIF1<0______.9．（2022春·福建·高三福建師大附中?？茧A段練習(xí)）設(shè)數(shù)列SKIPIF1<0的前SKIPIF1<0項(xiàng)和為SKIPIF1<0，若SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0______.10．（2022·四川達(dá)州·統(tǒng)考一模）已知正項(xiàng)數(shù)列SKIPIF1<0前SKIPIF1<0項(xiàng)和SKIPIF1<0滿足SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0__________.【沖刺提升】一、單選題1．（2022·陜西寶雞·統(tǒng)考一模）已知等差數(shù)列SKIPIF1<0滿足SKIPIF1<0，則下列命題：①SKIPIF1<0是遞減數(shù)列；②使SKIPIF1<0成立的SKIPIF1<0的最大值是9；③當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0取得最大值；④SKIPIF1<0，其中正確的是（

）A．①② B．①③C．①④ D．①②③2．（2022春·北京大興·高三統(tǒng)考期末）設(shè)SKIPIF1<0為等差數(shù)列SKIPIF1<0的前SKIPIF1<0項(xiàng)和.已知SKIPIF1<0，SKIPIF1<0，則（

）A．SKIPIF1<0為遞減數(shù)列 B．SKIPIF1<0C．SKIPIF1<0有最大值 D．SKIPIF1<03．（2023·河南鄭州·高三校聯(lián)考階段練習(xí)）等差數(shù)列SKIPIF1<0中，SKIPIF1<0，當(dāng)SKIPIF1<0取得最小值時(shí)，n的值為（

）A．4或5 B．5或6 C．4 D．54．（2022春·云南昆明·高三昆明市第三中學(xué)?？计谀┑缺葦?shù)列SKIPIF1<0滿足SKIPIF1<0，設(shè)數(shù)列SKIPIF1<0的前SKIPIF1<0項(xiàng)和為SKIPIF1<0，則SKIPIF1<0=（

）A．SKIPIF1<0 B．SKIPIF1<0 C．5 D．11二、多選題5．（2022春·廣東·高三校聯(lián)考階段練習(xí)）設(shè)數(shù)列SKIPIF1<0的前n項(xiàng)和為SKIPIF1<0，且SKIPIF1<0，若SKIPIF1<0，則下列結(jié)論正確的有（

）A．SKIPIF1<0B．當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0取得最小值C．當(dāng)SKIPIF1<0時(shí)，n的最小值為7D．當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0取得最小值三、填空題6．（2022春·云南昆明·高三昆明市第三中學(xué)校考期末）已知等差數(shù)列SKIPIF1<0的前SKIPIF1<0項(xiàng)和為SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0___________；7．（2020·全國(guó)·統(tǒng)考高考真題）記SKIPIF1<0為等差數(shù)列SKIPIF1<0的前n項(xiàng)和．若SKIPIF1<0，則SKIPIF1<0__________．8．（2022春·北京海淀·高三海淀實(shí)驗(yàn)中學(xué)?？茧A段練習(xí)）已知SKIPIF1<0是各項(xiàng)均為正的等比數(shù)列，SKIPIF1<0為其前SKIPIF1<0項(xiàng)和，若SKIPIF1<0，則公比SKIPIF1<0_______，SKIPIF1<0______．9．（2020·江蘇·統(tǒng)考高考真題）設(shè){an}是公差為d的等差數(shù)列，{bn}是公比為q的等比數(shù)列．已知數(shù)列{an+bn}的前n項(xiàng)和SKIPIF1<0，則d+q的值是_______．四、解答題10．（2022·全國(guó)·統(tǒng)考高考真題）已知SKIPIF1<0為等差數(shù)列，SKIPIF1<0是公比為2的等比數(shù)列，且SKIPIF1<0．(1)證明：SKIPIF1<0；(2)求集合SKIPIF1<0中元素個(gè)數(shù)．11．（2022春·河南·高三信陽高中校聯(lián)考期末）已知數(shù)列SKIPIF1<0的前SKIPIF1<0項(xiàng)和為SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，且當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0.(1)求數(shù)列SKIPIF1<0的通項(xiàng)公式；(2)設(shè)SKIPIF1<0，求數(shù)列SKIPIF1<0的前SKIPIF1<0項(xiàng)和SKIPIF1<0