數(shù)列加強(qiáng)
角度一:
1.(2018廣東一模)已知數(shù)列{an}的前n項(xiàng)和為Sn,且Sn=n2+n,則a5= .
2.(2018湖南、江西第二次聯(lián)考)已知Sn是數(shù)列{an}的前n項(xiàng)和,且log3Sn+1=n+1,則數(shù)列{an}的通項(xiàng)公式為 .
3.(2018湖南衡陽(yáng)一模)已知數(shù)列{an}前n項(xiàng)和為Sn,若Sn=2an-2n,則Sn= .
4.(2018河南適應(yīng)性考試)數(shù)列{an}中,an+Sn=3n-1,則{an}通項(xiàng)公式an= .
角度二:等差、等比數(shù)列性質(zhì)的應(yīng)用
1.(2018湖北武漢調(diào)研)在等差數(shù)列{an}中,前n項(xiàng)和Sn滿足S7-S2=45,則a5=( )
A.7 B.9 C.14 D.18
2.(2018安徽淮北二模)已知等比數(shù)列{an}中,a5=2,a6a8=8,則=( )
A.2 B.4 C.6 D.8
3.(2018山東煙臺(tái)期末)已知等比數(shù)列{an}中,a2a10=6a6,等差數(shù)列{bn}中,b4+b6=a6,則數(shù)列{bn}的前9項(xiàng)和為( )
A.9 B.27 C.54 D.72
4.(2018四川成都模擬)在等差數(shù)列{an}中,已知S8=100,S16=392,則S24= .
角度三:等差、等比數(shù)列的通項(xiàng)公式與前n項(xiàng)和公式的應(yīng)用
(1) 公式法
1.(2018四川南充三診)已知{an}是等比數(shù)列,a1=2,且a1,a3+1,a4成等差數(shù)列.
(1)求數(shù)列{an}的通項(xiàng)公式;
(2)若bn=log2an,求數(shù)列{bn}前n項(xiàng)的和.
2.(2017·北京卷) 已知等差數(shù)列{an}和等比數(shù)列{bn}滿足a1=b1=1,a2+a4=10,b2b4=a5.
(1)求{an}的通項(xiàng)公式;
(2)求和:b1+b3+b5+…+b2n-1.
(2)分組求和法 一個(gè)數(shù)列=(一個(gè)等差數(shù)列)+(一個(gè)等比數(shù)列)
3.(2018湖北重點(diǎn)高中期中)已知等差數(shù)列{an}的公差d為1,且a1,a3,a4成等比數(shù)列.
(1)求數(shù)列{an}的通項(xiàng)公式;
(2)設(shè)數(shù)列bn=求數(shù)列{bn}的前n項(xiàng)和Sn.
4.(2018河南焦作模擬)已知{an}為等差數(shù)列,且a2=3,{an}前4項(xiàng)的和為16,數(shù)列{bn}滿足b1=4,b4=88,且數(shù)列{bn-an}為等比數(shù)列.
(1)求數(shù)列{an}和{bn-an}的通項(xiàng)公式;
(2)求數(shù)列{bn}的前n項(xiàng)和Sn.
(3).裂項(xiàng)相消法
; ; = ; ; = ; ; .
5.數(shù)列{an}通項(xiàng)公式為(n∈N*),其前n項(xiàng)和為Sn,若Sn=9,則n= .
6.設(shè)數(shù)列{an}的前n項(xiàng)和為Sn,若Sn=4n2-1,則數(shù)列的前n項(xiàng)和為 .
7.已知函數(shù),正項(xiàng)數(shù)列{an}滿足a1=1,an ,n∈N*,且n≥2.
(1)求數(shù)列{an}的通項(xiàng)公式;
(2)對(duì)n∈N*,求的值.
(4).錯(cuò)位相減法 一個(gè)數(shù)列=(一個(gè)等差數(shù)列)*(一個(gè)等比數(shù)列)
8.(2018福建福州期末)已知數(shù)列{an}的前n項(xiàng)和為Sn,且Sn=2an-1.
(1)證明數(shù)列{an}是等比數(shù)列;
(2)設(shè)bn=(2n-1)an,求數(shù)列{bn}的前n項(xiàng)和Tn.
9.(2017·太原二模) 已知數(shù)列{an}的前n項(xiàng)和,數(shù)列{bn}滿足.
(1)求數(shù)列{bn}的通項(xiàng)公式;
(2)若,求數(shù)列{cn}的前n項(xiàng)和Tn.
角度四:由數(shù)列的遞推關(guān)系式求通項(xiàng)公式
考向1 形如an+1=an+f(n) (累加法)
10. (1)若數(shù)列{an}滿足a1=2,an+1=an+n+1,則數(shù)列{an}的通項(xiàng)公式為an= .
(2) 在數(shù)列{an}中,a1=1,an+1=an+2n,則通項(xiàng)公式為an= .
考向2 形如an+1=an·f(n) (累乘法)
11. (1)在數(shù)列{an}中,a1=1,an=an-1(n≥2),則通項(xiàng)公式為an= .
(2)在數(shù)列{an}中,a1=1,an+1=2nan,則通項(xiàng)公式為an= .