十年高考真题分类汇编(2010-2019) 数学 专题08 数列 (含答案)

(2)若S5=32,求λ.

32.(2015·北京·文T16)已知等差数列{an}满足a1+a2=10,a4-a3=2. (1)求{an}的通项公式;

(2)设等比数列{bn}满足b2=a3,b3=a7.问:b6与数列{an}的第几项相等? 33.(2015·重庆·文T16)已知等差数列{an}满足a3=2,前3项和S3=2. (1)求{an}的通项公式;

(2)设等比数列{bn}满足b1=a1,b4=a15,求{bn}的前n项和Tn. 34.(2015·福建·文T17)等差数列{an}中,a2=4,a4+a7=15. (1)求数列{an}的通项公式;

(2)设bn=2????-2+n,求b1+b2+b3+…+b10的值.

2

35.(2015·全国1·理T17)Sn为数列{an}的前n项和.已知an>0,????+2an=4Sn+3.

31

9

(1)求{an}的通项公式;

(2)设bn=????,求数列{bn}的前n项和.

????+1

36.(2015·安徽·文T18)已知数列{an}是递增的等比数列,且a1+a4=9,a2a3=8. (1)求数列{an}的通项公式; (2)设Sn为数列{an}的前n项和,bn=

????+1

,求数列{bn}的前n????????+1

1

项和Tn.

*

37.(2015·天津·理T18)已知数列{an}满足an+2=qan(q为实数,且q≠1),n∈N,a1=1,a2=2,且a2+a3,a3+a4,a4+a5成等差数列.

(1)求q的值和{an}的通项公式;

(2)设bn=??22??,n∈N,求数列{bn}的前n项和.

2??-1

*

????????

38.(2015·山东·文T19)已知数列{an}是首项为正数的等差数列,数列{??·??}的前n项和为2??+1. ????+1(1)求数列{an}的通项公式;

(2)设bn=(an+1)·2????,求数列{bn}的前n项和Tn.

39.(2015·浙江·文T17)已知数列{an}和{bn}满足a1=2,b1=1,an+1=2an(n∈N),b1+2b2+3b3+…+??bn=bn+1-1(n∈N).

(1)求an与bn;

(2)记数列{anbn}的前n项和为Tn,求Tn.

*

*

1??

111

9

40.(2015·天津·文T18)已知{an}是各项均为正数的等比数列,{bn}是等差数列,且a1=b1=1,b2+b3=2a3,a5-3b2=7. (1)求{an}和{bn}的通项公式;

(2)设cn=anbn,n∈N,求数列{cn}的前n项和.

41.(2015·湖北·文T19)设等差数列{an}的公差为d,前n项和为Sn,等比数列{bn}的公比为q,已知b1=a1,b2=2,q=d,S10=100.

(1)求数列{an},{bn}的通项公式;

(2)当d>1时,记cn=????,求数列{cn}的前n项和Tn.

??

*

??

42.(2014·全国2·理T17)已知数列{an}满足a1=1,an+1=3an+1. (1)证明:{????+2}是等比数列,并求{an}的通项公式; (2)证明:??+??+…+??<2.

??12

43.(2014·福建·文T17)在等比数列{an}中,a2=3,a5=81. (1)求an;

(2)设bn=log3an,求数列{bn}的前n项和Sn. 44.(2014·湖南·文T16)已知数列{an}的前n项和 Sn=

??2+??*

,n∈N. 21

1

1

3

1

(1)求数列{an}的通项公式;

(2)设bn=2????+(-1)an,求数列{bn}的前2n项和.

n

45.(2014·北京·文T14)已知{an}是等差数列,满足a1=3,a4=12,数列{bn}满足b1=4,b4=20,且{bn-an}为等比数列.

(1)求数列{an}和{bn}的通项公式; (2)求数列{bn}的前n项和.

46.(2014·大纲全国·理T18)等差数列{an}的前n项和为Sn.已知a1=10,a2为整数,且Sn≤S4. (1)求{an}的通项公式;

(2)设bn=????,求数列{bn}的前n项和Tn.

????+1

47.(2014·山东·理T19)已知等差数列{an}的公差为2,前n项和为Sn,且S1,S2,S4成等比数列. (1)求数列{an}的通项公式;

(2)令bn=(-1)????,求数列{bn}的前n项和Tn.

????+1

10

n-1

1

4??