第一篇:等差與等比數(shù)列綜合專題練習(xí)題
1.?dāng)?shù)列{an}是等差數(shù)列,若
值時(shí),n=()A.11a<-1,且它的前n項(xiàng)和Sn有最大值,那么當(dāng)Sn取得最小正a10
anB.17C.19D.21 2.已知公差大于0的等差數(shù)列{
求數(shù)列{an}的通項(xiàng)公式an. }滿足a2a4+a4a6+a6a2=1,a2,a4,a8依次成等比數(shù)列,3.已知△ABC中,三內(nèi)角A、B、C的度數(shù)成等差數(shù)列,邊a、b、c依次成等比數(shù)列.求證:△ABC是等邊三角形.
4.設(shè)無(wú)窮等差數(shù)列{an}的前n項(xiàng)和為Sn.是否存在實(shí)數(shù)k,使4Sn=(k+an)2對(duì)一切正整數(shù)n成立?若存在,求出k的值,并求相應(yīng)數(shù)列的通項(xiàng)公式;若不存在,說(shuō)明理由.
答:存在k=0,an=0或k=1,an=2n-1適合題意.
5.設(shè)數(shù)列{an}的前n項(xiàng)和為Sn,已知a1=1,Sn=nan﹣2n(n﹣1),(n∈N*)(Ⅰ)求證數(shù)列{an}為等差數(shù)列,并寫(xiě)出通項(xiàng)公式;(Ⅱ)是否存在自然數(shù)n,使得S1?S22?S3
3???Sn
n?400?
若存在,求出n的值;若不存在,說(shuō)明理由;
6.已知等差數(shù)列{an}的前n項(xiàng)和為Sn,且S10=55,S20=210.(1)求數(shù)列{an}的通項(xiàng)公式;
a(2)設(shè)bnm、k(k>m≥2,m,k∈N*),使得b1、bm、bk成等比數(shù)列?若存在,an+1
求出所有符合條件的m、k的值;若不存在,請(qǐng)說(shuō)明理由.
?2a1+9d=11?a1=1,??解:(1)設(shè)等差數(shù)列{an}的公差為d,即?,解得?所以an=a1+(n-1)d???2a1+19d=21?d=1.**2=n(n∈N).(2)假設(shè)存在m、k(k>m≥2,m,k∈N),使得b1、bm、bk成等比數(shù)列,則bm=
an1mkm21kb1bk.因?yàn)閎n=,所以b1=,bm=,bk=所以(=×.整理,22k+1an+1n+1m+1k+1m+1
2m2
得k=-m+2m+1
以下給出求m、k的方法:因?yàn)閗>0,所以-m2+2m+1>0,解得1-2 已知二次函數(shù)y=f(x)的圖象經(jīng)過(guò)坐標(biāo)原點(diǎn),其導(dǎo)函數(shù)為f(x)=3x2-2x,.數(shù)列{an}的前n項(xiàng)和為Sn,點(diǎn)(n,Sn)(n∈N*)均在函數(shù)y=f(x)的圖象上 3m(1)求數(shù)列{an}的通項(xiàng)公式;(2)設(shè)bn=,Tn是數(shù)列{bn}的前n項(xiàng)和,求使得Tn<對(duì)所20anan+1 有n∈N*都成立的最小正整數(shù)m.17.已知點(diǎn)(1是函數(shù)f(x)=ax(a>0,且a≠1)的圖象上一點(diǎn),等比數(shù)列{an}的前n項(xiàng)和為f(n)3 -c,數(shù)列{bn}的首項(xiàng)為c,且前n項(xiàng)和Sn滿足Sn-Sn-1Sn+Sn+1(n≥2).(1)求數(shù)列{an} 11000和{bn}的通項(xiàng)公式;(2)若數(shù)列{前n項(xiàng)和為T(mén)n,問(wèn)Tn>n是多少? 2009bnbn+1 8.已知定義域?yàn)镽的二次函數(shù)f(x)的最小值為0,且有f(1+x)=f(1-x),直線g(x)=4(x-1)的圖象被f(x)的圖象截得的弦長(zhǎng)為4,數(shù)列{an}滿足a1=2,(an+1-an)g(an)+f(an)=0 *(n∈N).(1)求函數(shù)f(x)的解析式;(2)求數(shù)列{an}的通項(xiàng)公式;(3)設(shè)bn=3f(an)-g(an+1),求數(shù)列{bn}的最值及相應(yīng)的n. 等差數(shù)列等比數(shù)列綜合練習(xí)題 一.選擇題 1.已知an?1?an?3?0,則數(shù)列?an?是() A.遞增數(shù)列 B.遞減數(shù)列 C.常數(shù)列 D.擺動(dòng)數(shù)列 2.等比數(shù)列{an}中,首項(xiàng)a1?8,公比q?,那么它的前5項(xiàng)的和S5的值是()A.31333537 B. C. D. 2222123.設(shè)Sn是等差數(shù)列{an}的前n項(xiàng)和,若S7=35,則a4=()A.8 B.7 C.6 D.5 4.等差數(shù)列{an}中,a1?3a8?a15?120,則2a9?a10?()A.24 B.22 C.20 D.-8 5.數(shù)列?an?的通項(xiàng)公式為an?3n2?28n,則數(shù)列?an?各項(xiàng)中最小項(xiàng)是()A.b7?a7,則b6b8?()A.2 B.4 C.8 D.16 10.已知等差數(shù)列?an?中, an?0,若m?1且am?1?am?1?am2?0,S2m?1?38,則m等于 A.38 B.20 C.10 D.9 11.已知sn是等差數(shù)列?an?(n?N*)的前n項(xiàng)和,且s6?s7?s5,下列結(jié)論中不正確的是()A.d<0 B.s11?0 C.s12?0 D.s13?0 12.等差數(shù)列{an}中,a1,a2,a4恰好成等比數(shù)列,則 a4的值是()a1 A.1 B.2 C.3 D.4 二.填空題 13.已知{an}為等差數(shù)列,a15=8,a60=20,則a75=________ 14.在等比數(shù)列{an}中,a2?a8?16,則a5=__________ 15.在等差數(shù)列{an}中,若a7=m,a14=n,則a21=__________ 16.若數(shù)列?xn?滿足lgxn?1?1?lgxn?n?N??,且x1?x2???x100?100,則lg?x101?x102???x200??________ 17.等差數(shù)列{an}的前n項(xiàng)和為Sn,若a3+a17=10,則S19的值_________ 18.已知等比數(shù)列{an}中,a1+a2+a3=40,a4+a5+a6=20,則前9項(xiàng)之和等于_________ 三.解答題 19.設(shè)三個(gè)數(shù)a,b,c成等差數(shù)列,其和為6,又a,b,c?1成等比數(shù)列,求此三個(gè)數(shù).20.已知數(shù)列?an?中,a1?1,an?2an?1?3,求此數(shù)列的通項(xiàng)公式.2an??s?5n?3n,求它的前3項(xiàng),并求它21.設(shè)等差數(shù)列的前n項(xiàng)和公式是n的通項(xiàng)公式.22.已知等比數(shù)列?an?的前n項(xiàng)和記為Sn,,S10=10, S30=70,求S40 Fpg 1.已知數(shù)列?an?是首項(xiàng)為a1?,公比q?141の等比數(shù)列,bn?2?3log1an 44(n?N*),數(shù)列?cn?滿足cn?an?bn. (1)求證:?bn?是等差數(shù)列; 2?an??a?2,a?a?6a?6(n?N),n?1nn2.?dāng)?shù)列滿足1設(shè)cn?log5(an?3). (Ⅰ)求證:?cn?是等比數(shù)列; *3.設(shè)數(shù)列?an?の前n項(xiàng)和為Sn,已知a1?2a2?3a3???nan?(n?1)Sn?2n(n?N).(2)求證:數(shù)列?Sn?2?是等比數(shù)列; 4.?dāng)?shù)列{an}滿足a1?1,an?12n?1an?(n?N?)nan?22n(1)證明:數(shù)列{}是等差數(shù)列; an2Sn25.?dāng)?shù)列?an?首項(xiàng)a1?1,前n項(xiàng)和Sn與an之間滿足an?(n?2) 2Sn?1(1)求證:數(shù)列??1??是等差數(shù)列 S?n?2,an?16.?dāng)?shù)列{an}滿足a1?3,an?1?(1)求證:{an?1}成等比數(shù)列; an?2*7.已知數(shù)列{an}滿足an?1?3an?4,(n?N)且a1?1,(Ⅰ)求證:數(shù)列?an?2?是等比數(shù)列; Fpg 本卷由系統(tǒng)自動(dòng)生成,請(qǐng)仔細(xì)校對(duì)后使用,答案僅供參考。 8. 數(shù)列{an}滿足:a1?1,n?an?1?(n?1)?an?n?(n?1),n?N*(1)證明:數(shù)列{an}是等差數(shù)列; n9.已知數(shù)列{an}の首項(xiàng)a1= 22an,an?1?,n=1,2,… 3an?1(1)證明:數(shù)列??1??1?是等比數(shù)列; ?an?1,Sn?n2an?n(n?1),n?1,2,L. 210.已知數(shù)列{an}の前n項(xiàng)和為Sn,a1?(1)證明:數(shù)列??n?1?Sn?是等差數(shù)列,并求Sn; n??11.(16分)已知數(shù)列{an}の前n項(xiàng)和是Sn,且Sn?2an?n(1)證明:?an?1?為等比數(shù)列; 12.?dāng)?shù)列{an}滿足:a1?2,a2?3,an?2?3an?1?2an(n?N?)(1)記dn?an?1?an,求證:數(shù)列{dn}是等比數(shù)列; 13.已知數(shù)列{an}の相鄰兩項(xiàng)an,an?1是關(guān)于x方程x2?2nx?bn?0の兩根,且a1?1.(1)求證:數(shù)列{an??2n}是等比數(shù)列; 14.(本題滿分12分)已知數(shù)列{an}中,a1?5且an?2an?1?2n?1(n?2且n?N*). 13?a?1?(Ⅰ)證明:數(shù)列?nn?為等差數(shù)列; ?2?15.已知數(shù)列?an?中,a1?1,an?1?an(n?N*)an?3(1)求證:??11???是等比數(shù)列,并求?an?の通項(xiàng)公式an;?an2?35,a3?,且當(dāng)n?2時(shí),24?16.設(shè)數(shù)列?an?の前n項(xiàng)和為Sn,n??.已知a1?1,a2?4Sn?2?5Sn?8Sn?1?Sn?1. (1)求a4の值; 答案第2頁(yè),總5頁(yè) Fpg(2)證明:?an?1???1?an?為等比數(shù)列; 2?17.設(shè)數(shù)列?an?の前n項(xiàng)和為Sn,且首項(xiàng)a1?3,an?1?Sn?3n(n?N?).n(Ⅰ)求證:Sn?3是等比數(shù)列; ??18.(本小題滿分10分)已知數(shù)列?an?滿足a1??1,an?1??a?2?(1)求證:數(shù)列?n?是等比數(shù)列; ?n?(3n?3)an?4n?6,n?N*. n 參考答案 1.(1)見(jiàn)解析;(2)Sn?2(3n?2)1n??();(3)m?1或m??5 334n?12a?5n2.(Ⅰ)見(jiàn)解析;(Ⅱ) 11Tn???2n.?3.;45?9(Ⅲ)3.(1)a2?4,a3?8; (2)見(jiàn)解析;(3)5 2nn?14.(1)詳見(jiàn)解析;(2)an?;(3)?2n?3?2?6 n?1?1(n?1)2?3. 5.(1)詳見(jiàn)解析;(2)?an??;(3)2?(n?2)3?(2n?1)(2n?3)?6.(1)證明{an?1}成等比數(shù)列の過(guò)程詳見(jiàn)試題解析; an?2Fpg 本卷由系統(tǒng)自動(dòng)生成,請(qǐng)仔細(xì)校對(duì)后使用,答案僅供參考。 (2)實(shí)數(shù)tの取值范圍為7.詳見(jiàn)解析 8.(1)見(jiàn)解析;(2)Sn1?33?1. ?t?222n?1??3n?1?3? ?49.(1)詳見(jiàn)解析(2)Sn?2?1nn?n?1??? 2n?12n2210.(1)由Sn?n2an?n(n?1)知,當(dāng)n?2時(shí),Sn?n,即(S(n?1)n?S?n1)?n(n2?1)Sn?n2Sn?1?n(n?1),所以所以?n?1n1?1Sn?Sn?1?1,對(duì)n?2成立.又S1?1,nn?11n?1?n?1?Sn?1?(n?1)?1,即Sn?是首項(xiàng)為1,公差為1の等差數(shù)列.所以n?n?n2Sn?. n?1(2)因?yàn)?/p> bn?Sn1111??(?)32n?3n(n?1)(n?3)2n?1n?3,所以b1?b2?L?bn?. 11111111115115(????L????)?(??)?22435nn?2n?1n?326n?2n?312?k?18?k?6?k?411.(1)見(jiàn)解析;(2)解析;(3)存在,?或?或?. m?5m?2m?18???12.(1)dn?1?2n?1(2)an?2n?1?1 ?2n?12?n為偶數(shù)??3313.(1)見(jiàn)解析;(2)Sn??,(3)(??,1) n?1?2?1n為奇數(shù)?3?314.(Ⅰ)詳見(jiàn)解析(Ⅱ)Sn?n?2n?1 15.(1)證明詳見(jiàn)解析;(2)?2???3. 7?1?16.(1);(2)證明見(jiàn)解析;(3)an??2n?1????8?2?17.(Ⅰ)詳見(jiàn)解析;(Ⅱ)(?9,3)?(3,??) n?1. 答案第4頁(yè),總5頁(yè) Fpg 18.(1)詳見(jiàn)解析(2)詳見(jiàn)解析 Fpg 本卷由系統(tǒng)自動(dòng)生成,請(qǐng)仔細(xì)校對(duì)后使用,答案僅供參考。 1.已知數(shù)列?an?是首項(xiàng)為a1?,公比q?141的等比數(shù)列,bn?2?3log1an 44(n?N*),數(shù)列?cn?滿足cn?an?bn. (1)求證:?bn?是等差數(shù)列; 2?an??a?2,a?a?6a?6(n?N),n?1nn2.?dāng)?shù)列滿足1設(shè)cn?log5(an?3). (Ⅰ)求證:?cn?是等比數(shù)列; *3.設(shè)數(shù)列?an?的前n項(xiàng)和為Sn,已知a1?2a2?3a3???nan?(n?1)Sn?2n(n?N).(2)求證:數(shù)列?Sn?2?是等比數(shù)列; 4.?dāng)?shù)列{an}滿足a1?1,an?12n?1an?(n?N?)nan?22n(1)證明:數(shù)列{}是等差數(shù)列; an2Sn25.?dāng)?shù)列?an?首項(xiàng)a1?1,前n項(xiàng)和Sn與an之間滿足an?(n?2) 2Sn?1(1)求證:數(shù)列??1??是等差數(shù)列 S?n?2,an?16.?dāng)?shù)列{an}滿足a1?3,an?1?(1)求證:{an?1}成等比數(shù)列; an?2*7.已知數(shù)列{an}滿足an?1?3an?4,(n?N)且a1?1,(Ⅰ)求證:數(shù)列?an?2?是等比數(shù)列; 答案第1頁(yè),總5頁(yè) 本卷由系統(tǒng)自動(dòng)生成,請(qǐng)仔細(xì)校對(duì)后使用,答案僅供參考。 8. 數(shù)列{an}滿足:a1?1,n?an?1?(n?1)?an?n?(n?1),n?N*(1)證明:數(shù)列{an}是等差數(shù)列; n9.已知數(shù)列{an}的首項(xiàng)a1= 22an,an?1?,n=1,2,… 3an?1(1)證明:數(shù)列??1??1?是等比數(shù)列; ?an?1,Sn?n2an?n(n?1),n?1,2,L. 210.已知數(shù)列{an}的前n項(xiàng)和為Sn,a1?(1)證明:數(shù)列??n?1?Sn?是等差數(shù)列,并求Sn; n??11.(16分)已知數(shù)列{an}的前n項(xiàng)和是Sn,且Sn?2an?n(1)證明:?an?1?為等比數(shù)列; 12.?dāng)?shù)列{an}滿足:a1?2,a2?3,an?2?3an?1?2an(n?N?)(1)記dn?an?1?an,求證:數(shù)列{dn}是等比數(shù)列; 13.已知數(shù)列{an}的相鄰兩項(xiàng)an,an?1是關(guān)于x方程x2?2nx?bn?0的兩根,且a1?1.(1)求證:數(shù)列{an??2n}是等比數(shù)列; 14.(本題滿分12分)已知數(shù)列{an}中,a1?5且an?2an?1?2n?1(n?2且n?N*). 13?a?1?(Ⅰ)證明:數(shù)列?nn?為等差數(shù)列; ?2?15.已知數(shù)列?an?中,a1?1,an?1?an(n?N*)an?3(1)求證:??11???是等比數(shù)列,并求?an?的通項(xiàng)公式an;?an2?35,a3?,且當(dāng)n?2時(shí),24?16.設(shè)數(shù)列?an?的前n項(xiàng)和為Sn,n??.已知a1?1,a2?4Sn?2?5Sn?8Sn?1?Sn?1. (1)求a4的值; 答案第2頁(yè),總5頁(yè) 本卷由系統(tǒng)自動(dòng)生成,請(qǐng)仔細(xì)校對(duì)后使用,答案僅供參考。 (2)證明:?an?1???1?an?為等比數(shù)列; 2?17.設(shè)數(shù)列?an?的前n項(xiàng)和為Sn,且首項(xiàng)a1?3,an?1?Sn?3n(n?N?).n(Ⅰ)求證:Sn?3是等比數(shù)列; ??18.(本小題滿分10分)已知數(shù)列?an?滿足a1??1,an?1??a?2?(1)求證:數(shù)列?n?是等比數(shù)列; ?n?(3n?3)an?4n?6,n?N*. n 參考答案 1.(1)見(jiàn)解析;(2)Sn?2(3n?2)1n??();(3)m?1或m??5 3342n?12.(Ⅰ)見(jiàn)解析;(Ⅱ)3.(1) an?511Tn???2n.?3.;45?9(Ⅲ)a2?4,a3?8; (2)見(jiàn)解析;(3)5 2nn?14.(1)詳見(jiàn)解析;(2)an?;(3)?2n?3?2?6 n?1?1(n?1)2?3. 5.(1)詳見(jiàn)解析;(2)?an??;(3)2?(n?2)3?(2n?1)(2n?3)?6.(1)證明{an?1}成等比數(shù)列的過(guò)程詳見(jiàn)試題解析; an?2答案第3頁(yè),總5頁(yè) 本卷由系統(tǒng)自動(dòng)生成,請(qǐng)仔細(xì)校對(duì)后使用,答案僅供參考。 (2)實(shí)數(shù)t的取值范圍為7.詳見(jiàn)解析 8.(1)見(jiàn)解析;(2)Sn1?33?1. ?t?222n?1??3n?1?3? ?49.(1)詳見(jiàn)解析(2)Sn?2?1nn?n?1??? 2n?12n2210.(1)由Sn?n2an?n(n?1)知,當(dāng)n?2時(shí),Sn?n,即(Sn?S(n?1)?n1)?n(n2?1)Sn?n2Sn?1?n(n?1),所以所以?n?1n1?1Sn?Sn?1?1,對(duì)n?2成立.又S1?1,nn?11n?1?n?1?Sn?1?(n?1)?1,即Sn?是首項(xiàng)為1,公差為1的等差數(shù)列.所以n?n?n2Sn?. n?1(2)因?yàn)?/p> bn?Sn1111??(?)32n?3n(n?1)(n?3)2n?1n?3,所以b1?b2?L?bn?. 11111111115115(????L????)?(??)?22435nn?2n?1n?326n?2n?312?k?18?k?6?k?411.(1)見(jiàn)解析;(2)解析;(3)存在,?或?或?. m?5m?2m?18???12.(1)dn?1?2n?1(2)an?2n?1?1 ?2n?12?n為偶數(shù)??3313.(1)見(jiàn)解析;(2)Sn??,(3)(??,1) n?1?2?1n為奇數(shù)?3?314.(Ⅰ)詳見(jiàn)解析(Ⅱ)Sn?n?2n?1 15.(1)證明詳見(jiàn)解析;(2)?2???3. 7?1?16.(1);(2)證明見(jiàn)解析;(3)an??2n?1????8?2?17.(Ⅰ)詳見(jiàn)解析;(Ⅱ)(?9,3)?(3,??) n?1. 答案第4頁(yè),總5頁(yè) 本卷由系統(tǒng)自動(dòng)生成,請(qǐng)仔細(xì)校對(duì)后使用,答案僅供參考。 18.(1)詳見(jiàn)解析(2)詳見(jiàn)解析 答案第5頁(yè),總5頁(yè) 等差等比數(shù)列問(wèn)題 一、等差數(shù)列、等比數(shù)列基本數(shù)列問(wèn)題 1.等差數(shù)列?an?,s6?36,sn?6?144,sn?324,求n的值 1)an?2an?1?1;2)an?2an?1?n?1;3)an?2an?1?n2?n?1; 4)an?2an?1?2n;5)an?2an?1?3n 1)sn?2an?1;2)sn?22n?1?n?1;3)sn?2an?1?n2?n?1; 4)sn?2an?1?2n;5)sn?2an?1?3n 2.已知數(shù)列,a?an?滿足:a=m(m為正整數(shù)) anA7n?5 2.已知兩個(gè)等差數(shù)列?an?和?bn?的前n項(xiàng)和分別為An,Bn,且n?,則使得為整數(shù) bnn?3Bn的的正整數(shù)n個(gè)數(shù)為: 3.已知等差數(shù)列?an?,a1?a3?a5???a99?36,公差d??2,求s100的值。 4、已知等差數(shù)列?an?的第2項(xiàng)為8,前10項(xiàng)和為185。1)求?an?的通項(xiàng)公式;2)若數(shù)列依次取出a2,a4,a8,?,a2n n?1 ?an?中 ?an當(dāng)a為偶數(shù)時(shí) ?n,若a6=1,則m所有??2 當(dāng)an為奇數(shù)時(shí)??3an?1 ?得到新數(shù)列?bn?,求數(shù)列?bn?的通項(xiàng)公式。 可能的取值為 四、數(shù)列與其它 1.已知數(shù)列?an?的通項(xiàng)公式an?n??n?N??,則數(shù)列?an?的前30項(xiàng)中,最大項(xiàng)和最小項(xiàng)分別 n?是 2.已知數(shù)列?an?是遞增數(shù)列,且an?n2??n,則實(shí)數(shù)3.(Ⅰ)設(shè) 4.設(shè)等比數(shù)列?an?的公比為q(q>0),它的前n項(xiàng)和為40,前2n項(xiàng)和為3280,且前前n項(xiàng)中數(shù)值最大的項(xiàng)為27,求數(shù)列的第前2n項(xiàng)。 5.已知數(shù)列?an?的首項(xiàng)為23,公差為整數(shù),且前6項(xiàng)為正,從第7項(xiàng)起為負(fù)數(shù),求Sn的最大值。 ?范圍是 an為正整數(shù),6.?dāng)?shù)列{an}為等差數(shù)列,其前n項(xiàng)和為Sn,數(shù)列{bn}為等比數(shù)列,且a1 數(shù)列{ban}是公比為64的等比數(shù)列,b2S2?64.(1)求an,bn;(2)求證1?1???1?3.S1S2Sn 4二、數(shù)列思想問(wèn)題 1.?dāng)?shù)列?an?的前n項(xiàng)和Sn,又bn2.求和sn? ?3,b1?1,a1,a2,??,an是各項(xiàng)均不為零的等差數(shù)列(n?4),且公差d?0,若將此數(shù)列刪 a1的數(shù)值;②求n的所有可d 去某一項(xiàng)得到的數(shù)列(按原來(lái)的順序)是等比數(shù)列:①當(dāng)n =4時(shí),求 能值; (Ⅱ)求證:對(duì)于一個(gè)給定的正整數(shù)n(n≥4),存在一個(gè)各項(xiàng)及公差都不為零的等差數(shù)列 ?an b1,b2,??,bn,其中任意三項(xiàng)(按原來(lái)順序)都不能組成等比數(shù)列.,求?bn?的前n項(xiàng)和 123n?2?3???n aaaa 3.等差數(shù)列?an?和等比?bn?,求數(shù)列?an?bn?的前n項(xiàng)和 4.1?1?1??? 1*2 2*3 3*4 ?n?1??n 12?13?24?3 ?????? n*n?11*22*33*4n*n?15.已知數(shù)列?an?滿足a1?2a2?3a3???nan?n?n?1?,求數(shù)列?an?的通項(xiàng)公式 三、復(fù)合數(shù)列問(wèn)題 1、已知數(shù)列?an?滿足下列條件,且a1?1,求數(shù)列?an?的通項(xiàng)公式第二篇:等差等比數(shù)列綜合練習(xí)題
第三篇:一輪復(fù)習(xí)等差等比數(shù)列證明練習(xí)題
第四篇:一輪復(fù)習(xí)等差等比數(shù)列證明練習(xí)題
第五篇:等差、等比數(shù)列問(wèn)題