设Sn是等差数列{an}的前n项和,若S3/S6=1/3,求S6/S12

来源:学生作业帮助网 编辑:六六作业网 时间:2024/11/08 11:19:19
设Sn是等差数列{an}的前n项和,若S3/S6=1/3,求S6/S12设Sn是等差数列{an}的前n项和,若S3/S6=1/3,求S6/S12设Sn是等差数列{an}的前n项和,若S3/S6=1/3

设Sn是等差数列{an}的前n项和,若S3/S6=1/3,求S6/S12
设Sn是等差数列{an}的前n项和,若S3/S6=1/3,求S6/S12

设Sn是等差数列{an}的前n项和,若S3/S6=1/3,求S6/S12
首先你要知道等差数列的顺次n项和性质
即Sn,S2n-Sn,S3n-S2n成公差为n²d的等差数列
则S6-S3=S3+9d
由S3/S6得S3=9d
则S6=27d d=S6/27
S9-S6=S6-S3+9d得S9=2S6
S12-S9=S9-S6+9d得S12=3S6+9d
得S6/S12=S6/(3S6+S6/3)=3/10

s6/s12=5/22

3S3=S6. S3,S6-S3,S9-S6,S12-S9仍为等差数列,所以S9=S6-S3+2(S6-S3)=6S3因为S3+S12-S9=(S6-S3)+(S9-S6),所以S12=2S9-2S3= 10S3所以S6/S12=3/10

在等差数列中有Sn,S2n-Sn,S3n-S2n……成等差数列
S6=3S3
S6-S3=2S3
S3,S6-S3,S9-S6,S12-S9成等差数列(证明见最后)
S9-S6=3S3 S12-S9=4S3
S9=S6+3S3=6S3
S12=S9+4S3=10S3
S6/S12=3S3/10S3=3/10
证明S3,S6-S3,S...

全部展开

在等差数列中有Sn,S2n-Sn,S3n-S2n……成等差数列
S6=3S3
S6-S3=2S3
S3,S6-S3,S9-S6,S12-S9成等差数列(证明见最后)
S9-S6=3S3 S12-S9=4S3
S9=S6+3S3=6S3
S12=S9+4S3=10S3
S6/S12=3S3/10S3=3/10
证明S3,S6-S3,S9-S6,S12-S9成等差数列
S3=A1+A2+A3
S6-S3=A4+A5+A6=(A1+3d)+(A2+3d)+(A3+3d)=A1+A2+A3+9d=S3+9d
S9-S6=A7+A8+A9=A1+A2+A3+18d=S3+18d
S12-S9=A10+A11+A12=A1+A2+A3+27d=S3+27d
S3,S6-S3,S9-S6,S12-S9成等差数列

收起

只能估计d=2

设Sn为等差数列{An}的前n项和,求证:{Sn/n}是等差数列 设Sn是等差数列{an}的前n项和,求证:若正整数m,n,p成等差数列,则Sm/m,Sn/n,Sp/p也成等差数列. 设Sn为等差数列an的前n项和.求证Sn/n为等差数列 设等差数列{an}的前n项和为Sn 若a1=Sn> 设等比数列an的公比为q,前n项和为sn,若s(n+1),sn,s(n+2)成等差数列,求q的值 设等比数列[an]的公比为q,前n项和为Sn,若S(n+1),Sn,S(n+2)成等差数列,则q的值? 设等比数列 {an} 的公比为q,前n项和为Sn,若S(n+1),Sn,S(n+2)成等差数列,则q= 设Sn是等差数列{an}的前n项和,已知S8=108,Sn=630,S(n-8)=234,求n. 设Sn是等差数列{an}的前n项和,已知S8=108,Sn=630,S(n-8)=234,求n. 设数列{an}的前n项和为Sn,若对任意正整数,都有Sn=n(a1+an)/2,证明{an}是等差数列. 若等差数列{an}的前n项和为Sn,且满足Sn/S2n为常数,则称该数列为S数列 若首项为a1的各项为正数的等差数列{an}是S数列,设n+h=2008,(n,h为正数) 求1/Sn+1/Sh的最小值 Sn、Sh分别是数列的前n项和和    1.(1) 设Sn是等差数列{an}的前n项和,若a5:a3=5:9,则S9:S5=_________(2) 设Sn,Tn是等差数列{an}{bn}的前n项和,若Sn:Tn=(2n+1):(n+2),a10:b10=_2.设数列{an}的通项公式为an=2,(n=1);3n-4,(n>=2),求{an}的前n项和S 设Sn是等差数列{an}的前n项和,且S5S8,则a1 设{an}是等差数列前n项和为Sn,若S4>=10,S5 数列{an}满足a(n+1)+an=4n-3,若{an}是等差数列,(1)求{an}的通项公式(2)设Sn是{an}的前n项和,数列{an}满足a(n+1)+an=4n-3,若{an}是等差数列,(1)求{an}的通项公式(2)设Sn是{an}的前n项和,且a1=1,求S(2n+1) 设an是公比为q的等比数列,Sn是它的前n项的和,若S(n+1),Sn,S(n+2)成等差数列,则公比q= 设数列{an}的前n项和为sn,若对于所有的正整数n,都有sn=n(a1+an)/2,证明{an}是等差数列设数列{an}的前n项和为sn,若对于所有的正整数n,都有sn=n(a1+an)/2,证明{an}是等差数列 设等差数列an的前n项和为Sn,若S4>=10,S5