新高考數(shù)學(xué)一輪復(fù)習(xí)精講精練4.3 利用遞推公式求通項(xiàng)（基礎(chǔ)版）（原卷版）

4.3利用遞推公式求通項(xiàng)（精講）（基礎(chǔ)版）思維導(dǎo)圖思維導(dǎo)圖考點(diǎn)呈現(xiàn)考點(diǎn)呈現(xiàn)例題剖析例題剖析考點(diǎn)一累加法【例1-1】（2022·四川成都）已知數(shù)列SKIPIF1<0滿足SKIPIF1<0，則an=【例1-2】（2022·全國(guó)·高三專題練習(xí)）在數(shù)列SKIPIF1<0中，SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0等于（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0【一隅三反】1．（2022·全國(guó)·高三專題練習(xí)）數(shù)列SKIPIF1<0滿足SKIPIF1<0，且SKIPIF1<0，則數(shù)列SKIPIF1<0的通項(xiàng)公式為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．（2022·山東·濟(jì)南市歷城第二中學(xué)模擬預(yù)測(cè)）數(shù)列SKIPIF1<0中，SKIPIF1<0且SKIPIF1<0，則SKIPIF1<0_________.3．（2022·全國(guó)·高三專題練習(xí)）設(shè)數(shù)列SKIPIF1<0滿足SKIPIF1<0，則SKIPIF1<0=_______.考點(diǎn)二累乘法【例2】（2022·全國(guó)·高三專題練習(xí)）已知數(shù)列SKIPIF1<0滿足SKIPIF1<0，SKIPIF1<0(SKIPIF1<0，SKIPIF1<0)，則數(shù)列SKIPIF1<0的通項(xiàng)SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0【一隅三反】1．（2022·黑龍江·齊齊哈爾市第一中學(xué)校一模（文））數(shù)列SKIPIF1<0中，SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，則數(shù)列SKIPIF1<0的通項(xiàng)公式為______．2．（2022·全國(guó)·高三專題練習(xí)）設(shè)數(shù)列SKIPIF1<0是首項(xiàng)為1的正項(xiàng)數(shù)列，且SKIPIF1<0，則它的通項(xiàng)公式SKIPIF1<0______.3（2022·全國(guó)·高三專題練習(xí)）已知數(shù)列SKIPIF1<0滿足SKIPIF1<0，SKIPIF1<0，則數(shù)列SKIPIF1<0的通項(xiàng)公式為SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0．考點(diǎn)三公式法【例3-1】（2022·上海市）數(shù)列SKIPIF1<0滿足SKIPIF1<0，SKIPIF1<0，則數(shù)列SKIPIF1<0的通項(xiàng)公式為______．【例3-2】（2022·全國(guó)·高三階段練習(xí)（理））已知數(shù)列SKIPIF1<0滿足SKIPIF1<0，SKIPIF1<0，則數(shù)列SKIPIF1<0的通項(xiàng)公式為___________.【一隅三反】1．（2022·上海民辦南模中學(xué)高三階段練習(xí)）已知數(shù)列SKIPIF1<0的前n項(xiàng)和SKIPIF1<0，則數(shù)列SKIPIF1<0的通項(xiàng)公式為______．2．（2022·廣西·模擬預(yù)測(cè)（理））正項(xiàng)數(shù)列SKIPIF1<0的前SKIPIF1<0項(xiàng)和為SKIPIF1<0，且有SKIPIF1<0，則SKIPIF1<0___________．3．（2022·云南·昆明一中高三階段練習(xí)（理））已知數(shù)列SKIPIF1<0滿足SKIPIF1<0，則SKIPIF1<0___________.考點(diǎn)四構(gòu)造等差數(shù)列【例4-1】（2022·四川省綿陽南山中學(xué)）已知數(shù)列SKIPIF1<0滿足SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則an=【例4-2】（2022·江西）已知數(shù)列SKIPIF1<0滿足：SKIPIF1<0，SKIPIF1<0（SKIPIF1<0，SKIPIF1<0），則SKIPIF1<0___________.【例4-3】（2022·全國(guó)·高三專題練習(xí)）已知數(shù)列SKIPIF1<0滿足SKIPIF1<0，求出數(shù)列SKIPIF1<0的通項(xiàng)公式；【一隅三反】1．（2022·全國(guó)·課時(shí)練習(xí)）已知數(shù)列SKIPIF1<0滿足SKIPIF1<0，且SKIPIF1<0，則數(shù)列SKIPIF1<0__________2．（2022·全國(guó)·高三專題練習(xí)）已知數(shù)列SKIPIF1<0滿足SKIPIF1<0，且SKIPIF1<0，則數(shù)列SKIPIF1<0的通項(xiàng)公式SKIPIF1<0______．3．（2022·全國(guó)·高三專題練習(xí)）已知數(shù)列SKIPIF1<0的首項(xiàng)SKIPIF1<0，且各項(xiàng)滿足公式SKIPIF1<0，則數(shù)列SKIPIF1<0的通項(xiàng)公式為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0考點(diǎn)五構(gòu)造等比數(shù)列【例5】（2022·安徽）設(shè)SKIPIF1<0為數(shù)列SKIPIF1<0的前SKIPIF1<0項(xiàng)和，若SKIPIF1<0SKIPIF1<0，則SKIPIF1<0______．【一隅三反】1．（2022·全國(guó)·高二課時(shí)練習(xí)）在數(shù)列SKIPIF1<0中，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則該數(shù)列的通項(xiàng)公式SKIPIF1<0______．2．（2022·上海市控江中學(xué)）已知數(shù)列SKIPIF1<0滿足SKIPIF1<0，則其通項(xiàng)公式SKIPIF1<0_______．3．（2022·福建省長(zhǎng)汀縣第一中學(xué)）已知數(shù)列SKIPIF1<0滿足SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0的前n項(xiàng)和為_____.4.3利用遞推公式求通項(xiàng)（精練）（基礎(chǔ)版）題組一題組一累加法1．（2022·陜西·無高三階段練習(xí)）若數(shù)列SKIPIF1<0滿足SKIPIF1<0且SKIPIF1<0，則數(shù)列SKIPIF1<0的第100項(xiàng)為（

）A．2 B．3 C．SKIPIF1<0 D．SKIPIF1<02．（2022·四川·樹德中學(xué)）已知數(shù)列SKIPIF1<0滿足SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0的最小值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022·全國(guó)·高三專題練習(xí)）已知數(shù)列SKIPIF1<0滿足SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·全國(guó)·高三專題練習(xí)）數(shù)列SKIPIF1<0滿足SKIPIF1<0，且SKIPIF1<0（SKIPIF1<0），則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．（2022·全國(guó)·高三專題練習(xí)）在數(shù)列{an}中，a1＝1，an＋1＝an＋2n，則通項(xiàng)公式an＝________．6．（2022·全國(guó)·高三專題練習(xí)）已知SKIPIF1<0，求通項(xiàng)SKIPIF1<0=.7．（2022·重慶·模擬預(yù)測(cè)）已知數(shù)列SKIPIF1<0滿足SKIPIF1<0.(1)求證：SKIPIF1<0是等差數(shù)列；(2)若SKIPIF1<0，求SKIPIF1<0的通項(xiàng)公式.題組二題組二累乘法1．（2022·全國(guó)·高三專題練習(xí)）在數(shù)列{an}中，a1=1，SKIPIF1<0(n≥2)，求數(shù)列{an}的通項(xiàng)公式.2．（2022·全國(guó)·高三專題練習(xí)）已知數(shù)列SKIPIF1<0滿足SKIPIF1<0，SKIPIF1<0，求數(shù)列SKIPIF1<0的通項(xiàng)公式.3．（2022·全國(guó)·高三專題練習(xí)）數(shù)列SKIPIF1<0滿足：SKIPIF1<0，SKIPIF1<0，求SKIPIF1<0的通項(xiàng)公式.4．（2022·全國(guó)·高三專題練習(xí)）在數(shù)列SKIPIF1<0中，SKIPIF1<0，求數(shù)列SKIPIF1<0的通項(xiàng)公式.5．（2022·全國(guó)·高三專題練習(xí)）已知數(shù)列SKIPIF1<0的首項(xiàng)為SKIPIF1<0，且滿足SKIPIF1<0.求SKIPIF1<0的通項(xiàng)公式.題組三題組三公式法1．（2022·全國(guó)·高三專題練習(xí)）已知SKIPIF1<0為數(shù)列SKIPIF1<0的前n項(xiàng)積，若SKIPIF1<0，則數(shù)列SKIPIF1<0的通項(xiàng)公式SKIPIF1<0（

）A．3-2n B．3+2n C．1+2n D．1-2n2．（2022·湖北省武漢市漢鐵高級(jí)中學(xué)高三階段練習(xí)）(多選）數(shù)列SKIPIF1<0的前SKIPIF1<0項(xiàng)為SKIPIF1<0，已知SKIPIF1<0，下列說法中正確的是（

）A．SKIPIF1<0為等差數(shù)列 B．SKIPIF1<0可能為等比數(shù)列C．SKIPIF1<0為等差數(shù)列或等比數(shù)列 D．SKIPIF1<0可能既不是等差數(shù)列也不是等比數(shù)列3．（2022·全國(guó)·高三專題練習(xí)）若數(shù)列SKIPIF1<0滿足SKIPIF1<0,SKIPIF1<0,則SKIPIF1<0______．4．（2022·全國(guó)·高三專題練習(xí)）已知數(shù)列SKIPIF1<0滿足SKIPIF1<0，SKIPIF1<0.數(shù)列SKIPIF1<0的通項(xiàng)公式.5．（2022·四川·什邡中學(xué)）數(shù)列SKIPIF1<0的前SKIPIF1<0項(xiàng)和SKIPIF1<0，則它的通項(xiàng)公式是_______．6．（2022·安徽宿州）已知數(shù)列SKIPIF1<0的前n項(xiàng)和為SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0的通項(xiàng)公式為SKIPIF1<0______．7．（2022·北京交通大學(xué)附屬中學(xué)高二期中）已知數(shù)列SKIPIF1<0滿足SKIPIF1<0，則SKIPIF1<0____.8．（2022·山西太原·二模（文））已知數(shù)列SKIPIF1<0的首項(xiàng)為1，前n項(xiàng)和為SKIPIF1<0，且SKIPIF1<0，則數(shù)列SKIPIF1<0的通項(xiàng)公式SKIPIF1<0___________.題組四題組四構(gòu)造等差數(shù)列1．（2022·全國(guó)·課時(shí)練習(xí)）在數(shù)列SKIPIF1<0中，若SKIPIF1<0，則SKIPIF1<0________.2．（2022·湖北·荊州中學(xué)）已知數(shù)列SKIPIF1<0滿足SKIPIF1<0，且SKIPIF1<0．則數(shù)列SKIPIF1<0的通項(xiàng)公式為SKIPIF1<0_______．3．（2022·全國(guó)·課時(shí)練習(xí)）已知數(shù)列SKIPIF1<0中，SKIPIF1<0，求數(shù)列SKIPIF1<0的通項(xiàng)公式；4．（2022·全國(guó)·高三專題練習(xí)）已知數(shù)列SKIPIF1<0中，SKIPIF1<0，SKIPIF1<0