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1、.高考專題復(fù)習(xí):數(shù)列(文)學(xué)校:___________姓名:___________班級(jí):___________考號(hào):___________一、選擇題(題型注釋)1.?dāng)?shù)列滿足,則與的等比中項(xiàng)是(A)(B)(C)(D)2.已知成等比數(shù)列,分別成等差數(shù)列,且,則的值等于()A.1B.2C.3D.43.已知等比數(shù)列中,則其前3項(xiàng)的和的取值范圍是()A. B.?。? D.4.已知等比數(shù)列中,,,公比,則()A.B.C.D.5.在等比數(shù)列中,若,則()A.B.C.D.6.設(shè)等差數(shù)列的前項(xiàng)和為,若,,,則()A.3B.4C.5D.67.已知等差數(shù)列的前
2、項(xiàng)和為,且,則()A.B.C.D.8.等差數(shù)列中,,是前n項(xiàng)和且,則當(dāng)()時(shí),最大.A.12B.13C.12或13D.13或149.等比數(shù)列的各項(xiàng)均為正數(shù),且,則()A.B.C.D.10.等差數(shù)列的前項(xiàng)和為,若,則()A.55 B.95 C.100D.不能確定11.為等差數(shù)列的前項(xiàng)和,,則()A.B.C.D.12.等比數(shù)列中,,則數(shù)列的前8項(xiàng)和等于()....A.6B.5C.3D.413.已知等差數(shù)列中,,則的值是()A.15B.30C.31D.6414.已知各項(xiàng)不為的等差數(shù)列滿足,數(shù)列是等比數(shù)列,且,則()A.B.C.D.15.在等
3、差數(shù)列中,若,,則等于()A.B.C.D.16.等差數(shù)列{an}中,,{bn}為等比數(shù)列,且b7=a7,則b6b8的值為()A.4B.2C.16D.817.已知等差數(shù)列滿足,則()A.B.C.D.18.?dāng)?shù)列滿足,且,則()A.B.C.D.19.已知數(shù)列的前項(xiàng)和為,且,則等于()A.7B.8C.15D.1620.在等比數(shù)列中,若,則=()A.B.C.D.921.已知數(shù)列{an}中,,,則的值為()A.49B.50C.51D.52二、填空題22.已知數(shù)列滿足,則的前n項(xiàng)和_____23.在數(shù)列中,,則數(shù)列的通項(xiàng)=____24.在數(shù)列中,已知,
4、,且數(shù)列是等比數(shù)列,則25.已知公差不為的等差數(shù)列,其前n項(xiàng)和為,若成等比數(shù)列,則的值為.26.已知等比數(shù)列的前項(xiàng)和為,若,則等于.27.已知等比數(shù)列中,,,則該數(shù)列的通項(xiàng)公式....,數(shù)列的前項(xiàng)的和為.三、解答題(題型注釋)28.已知等比數(shù)列中,,(1)求數(shù)列的通項(xiàng)公式;(2)設(shè)等差數(shù)列中,,求數(shù)列的前項(xiàng)和。29.已知數(shù)列的前項(xiàng)和為,且.(1)求數(shù)列的通項(xiàng)公式;(2)設(shè),求數(shù)列的前項(xiàng)和為.....30.各項(xiàng)均為正數(shù)的數(shù)列中,,是數(shù)列的前項(xiàng)和,對(duì)任意,有()(1)求常數(shù)的值;(2)求數(shù)列的通項(xiàng)公式;(3)記,求數(shù)列的前項(xiàng)和31.設(shè)是公比大
5、于1的等比數(shù)列,為數(shù)列的前項(xiàng)和.已知,且構(gòu)成等差數(shù)列.(Ⅰ)求數(shù)列的通項(xiàng)公式;(Ⅱ)令,求數(shù)列的前項(xiàng)和.....32.已知等差數(shù)列的前項(xiàng)和滿足,.(1)求的通項(xiàng)公式;(2)求數(shù)列的前項(xiàng)和.33.已知等差數(shù)列中,,.(Ⅰ)求數(shù)列的通項(xiàng)公式;(Ⅱ)若,求數(shù)列的前項(xiàng)和.....34.已知等差數(shù)列的公差,前項(xiàng)和為,等比數(shù)列滿足,,.(1)求,;(2)記數(shù)列的前項(xiàng)和為,求.35.已知各項(xiàng)均為正數(shù)的數(shù)列前n項(xiàng)和為,首項(xiàng)為,且成等差數(shù)列.(1)求數(shù)列的通項(xiàng)公式;(2)若,設(shè),求數(shù)列的前項(xiàng)和.....36.已知等差數(shù)列首項(xiàng),公差為,且數(shù)列是公比為的等比數(shù)
6、列.(1)求;(2)求數(shù)列的通項(xiàng)公式及前項(xiàng)和;(3)求數(shù)列的前項(xiàng)和.37.已知數(shù)列滿足,.(Ⅰ)求證為等比數(shù)列,并數(shù)列的通項(xiàng)公式;(Ⅱ)求數(shù)列的前項(xiàng)和.....38.設(shè)數(shù)列的前n項(xiàng)和為.已知.(I)求的通項(xiàng)公式;(II)若數(shù)列滿足,求的前n項(xiàng)和.39.已知等差數(shù)列的前項(xiàng)和滿足(1)求的通項(xiàng)公式;(2)求數(shù)列的前項(xiàng)和.....40.?dāng)?shù)列的前項(xiàng)和為,且,數(shù)列滿足,.(1)求數(shù)列的通項(xiàng)公式;(2)求證:數(shù)列為等比數(shù)列,并求數(shù)列的通項(xiàng)公式;(3)設(shè)數(shù)列滿足,其前項(xiàng)和為,求.....參考答案1.D2.B3.D4.B5.A6.C7.B8.D9.B10
7、.B11.B12.D13.A14.D15.B16.A17.B18.A19.C20.B21.D22.23.n224.25.226.127.28.(1)設(shè)等比數(shù)列的公比為由已知得(2)由(1)得設(shè)等差數(shù)列的公差為,則29.(1)由可求得數(shù)列的通項(xiàng)公式;(2)首先整理,確定數(shù)列的通項(xiàng)公式,依據(jù)特點(diǎn)采用錯(cuò)位相減法求和試題解析:(1)當(dāng)時(shí),得.當(dāng)時(shí),,當(dāng)時(shí),也滿足.∴.(2),則,利用錯(cuò)位相減法可算得.30.(1)∵,對(duì)任意的,有....∴,即,∴……4分(2)當(dāng)時(shí),①②……6分①-②得:∵,∴,∴……9分(3)∴……11分③又④③-④得:……14
8、分31.(Ⅰ)由已知得解得.設(shè)數(shù)列的公比為,由,可得.又,可知,即,解得.由題意得..故數(shù)列的通項(xiàng)為.………………………………6分(Ⅱ)由于,所以兩式相減得:………………………………12分..