第頁(yè)高二上學(xué)期期末復(fù)習(xí)第四章題型歸納（拔尖篇）題型1根據(jù)數(shù)列的遞推公式求數(shù)列的項(xiàng)、通項(xiàng)公式題型1根據(jù)數(shù)列的遞推公式求數(shù)列的項(xiàng)、通項(xiàng)公式1．已知數(shù)列an，滿足an?an?1=2，A．18 B．36 C．72 D．1442．已知數(shù)列an的項(xiàng)滿足an+1=nn+2anA．2n+12 B．2nn+1 C．3．已知數(shù)列an滿足a1=2(1)求數(shù)列an(2)設(shè)bn=nan2n，且數(shù)列bn的前題型2題型2數(shù)列的周期性的應(yīng)用1．已知數(shù)列an滿足a1=3,an+1A．3 B．12 C．?132．已知數(shù)列an的前n項(xiàng)和為Sn,anA．1012 B．?1012 C．2023 D．?2023題型3題型3求數(shù)列的最大項(xiàng)、最小項(xiàng)1．若數(shù)列an的前n項(xiàng)積Tn=1?215A．?3 B．?1 C．2 D．32．已知數(shù)列an的前n項(xiàng)和為Sn，(1)求數(shù)列an的通項(xiàng)公式a(2)若數(shù)列bn滿足：bn=題型4題型4等差數(shù)列的判定與證明1．“a3+a9=2A．充分不必要條件 B．必要不充分條件C．充要條件 D．既不充分又不必要條件2．已知數(shù)列an滿足an+A．a(chǎn)n B．a(chǎn)2n?1 C．a(chǎn)2n3．設(shè)Sn為數(shù)列an的前n項(xiàng)和，Tn為數(shù)列Sn的前(1)求S1，S(2)求證：數(shù)列1S(3)求數(shù)列an4．已知數(shù)列an中，a1=2(1)證明數(shù)列1an?1(2)若對(duì)任意n∈N?，都有a1題型5題型5利用等差數(shù)列的性質(zhì)解題1．?dāng)?shù)列an是等差數(shù)列，若a3=3,1aA．52 B．5 C．9 2．已知等差數(shù)列an滿足a3+a6A．－3 B．3 C．－12 D．12題型6題型6求等差數(shù)列的前n項(xiàng)和及其最值1．等差數(shù)列an的前n項(xiàng)和為Sn，且a1+aA．63 B．45 C．49 D．562．等差數(shù)列an是遞增數(shù)列，公差為d，前n項(xiàng)和為Sn，滿足a7A．d<0 B．a(chǎn)C．當(dāng)n=5時(shí)Sn最小 D．Sn>0時(shí)題型7題型7等比數(shù)列的判定與證明1．在數(shù)列an中,a1=14,aA．a(chǎn)n2n+3是等比數(shù)列C．a(chǎn)n2n+32．已知數(shù)列an的前n項(xiàng)和為Sn,a1=1,Sn+1=①an+1是等差數(shù)列

②an+1是等比數(shù)列

③aA．①③ B．②③ C．①④ D．②④3．在數(shù)列an中，a1=1(1)證明an(2)若bn=log2an+1題型8題型8等比數(shù)列性質(zhì)的應(yīng)用1．已知正項(xiàng)等比數(shù)列an的前n項(xiàng)積為Mn，且M2024=3M2019，若A．15 B．25 C．352．在等比數(shù)列an中，如果a1+a2=16，A．40 B．36 C．54 D．81題型9題型9求等比數(shù)列的前n項(xiàng)和及其最值1．已知數(shù)列an的前n項(xiàng)和為Sn，且a3=2，A．?dāng)?shù)列an為等比數(shù)列 B．?dāng)?shù)列SC．S100=322．已知數(shù)列an的前n項(xiàng)和為S(1)求數(shù)列an(2)設(shè)bn=n?1n+1an，求數(shù)列題型10題型10等差、等比數(shù)列的綜合應(yīng)用1．已知等差數(shù)列an的公差不為0，設(shè)bi=anii∈N?，若n2=2A．a(chǎn)81 B．a(chǎn)121 C．a(chǎn)1222．已知Sn是等差數(shù)列{an}的前n項(xiàng)和，公差d≠0，a1A．136 B．2 C．10?1 3．已知等差數(shù)列an的前n項(xiàng)和為Sn，公差d≠0，且S3+S5=50(1)求數(shù)列an(2)設(shè)bn①求數(shù)列bn的前n項(xiàng)和T②若不等式λTn?Sn題型11題型11數(shù)列的求和1．已知函數(shù)fx滿足fx+f1?x=2(1)求數(shù)列an(2)若數(shù)列bn滿足b1=23，bn=1an?an+1（n≥22．已知等差數(shù)列an滿足：a1=1，d=2，數(shù)列bn滿足b1(1)證明：數(shù)列bn(2)若數(shù)列cn滿足cn=an4n?13．已知數(shù)列an滿足a1=3(1)證明數(shù)列an?n是等比數(shù)列，并求出數(shù)列(2)設(shè)bn=1log2an?n，數(shù)列bnbn+1第四章數(shù)列全章綜合測(cè)試卷（提高篇）1．已知數(shù)列{an}，{bn}滿足：bn=aA．a(chǎn)n=2n?3 B．a(chǎn)n=n22．已知數(shù)列{an}是等差數(shù)列，數(shù)列{bn}是等比數(shù)列，a7A．π4 B．π3 C．π23．已知遞增數(shù)列an的前n項(xiàng)和Sn滿足2Sn=nan+1，n∈N*，設(shè)A．2023 B．2024 C．4045 D．80894．已知數(shù)列{an}滿足2a1+22aA．a(chǎn)1的值為2B．?dāng)?shù)列{aC．?dāng)?shù)列{an}為遞減數(shù)列5．已知an是各項(xiàng)均為正數(shù)的無(wú)窮數(shù)列，其前n項(xiàng)和為Sn，①a2=2；③nan>(n+1)an+1；其中所有正確結(jié)論的序號(hào)是．6．已知各項(xiàng)均為正數(shù)的數(shù)列an的前n項(xiàng)和為Sn，且4Sn=an+3an?1，數(shù)列bn滿足7．記Sn為數(shù)列an的前n項(xiàng)和，已知a1(1)求an(2)令bn=18．已知數(shù)列an的前n項(xiàng)和為Sn，a1(1)證明：數(shù)列an(2)若______，求數(shù)列bn的前n項(xiàng)和T從①bn=nan；②9．已知橫坐標(biāo)為t的點(diǎn)P