设等差数列{an}的前n项和为Sn,且a3+a7-a10=8,a11-a4=4,则S13等于?

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/04 12:52:33
设等差数列{an}的前n项和为Sn,且a3+a7-a10=8,a11-a4=4,则S13等于?

设等差数列{an}的前n项和为Sn,且a3+a7-a10=8,a11-a4=4,则S13等于?
设等差数列{an}的前n项和为Sn,且a3+a7-a10=8,a11-a4=4,则S13等于?

设等差数列{an}的前n项和为Sn,且a3+a7-a10=8,a11-a4=4,则S13等于?
方法1:设公差为d,
a3+a7-a10=a1+2d+a1+6d-(a1+9d)=2a1-d=8
a11-a4=a1+10d-(a1+3d)=7d=4
d=4/7
a1=60/7
a13=a1+12d=108/7
S13=(a1+a13)×13/2=156
方法2:两式相加:a3+a7-a10+a11-a4=12
a7+(a3-a4)-(a10-a11)=12
因为a3-a4=a10-a11=-d
因此结果为a7.
所以a7=12
S13=a1+a13+a2+a12+a3+a11+...+a7
因为a1+a13=a2+a12=a3+a11=...=2a7
所以S13=13a7=156
不好意思,刚才口算错误

设Sn为等差数列an的前n项和.求证Sn/n为等差数列 设Sn为等差数列{An}的前n项和,求证:{Sn/n}是等差数列 设等差数列{an}的前n项和为Sn,且满足S15>0,S16 设等差数列{an}的前n项和为Sn,且S6 设等差数列{an}前n项和为Sn,且a1>0,S13=S19,求Sn的最大值 设等差数列An的前n项和为Sn,且S4=4S2,A2n=2An+1 设数列{an}为正项数列,前n项的和为Sn,且an,Sn,an^2成等差数列,求an通项公式 设等差数列{an}的前n项和为Sn,且S5=-5,S10=15,求数列{Sn/n}的前n项和Tn 设等差数列{an}的前n项和为Sn 若a1=Sn> 设等差数列an前n项和为sn,且s10=s20.则s30=? 等差数列an的前n项和为Sn,已知Sm=a,Sn-Sn-m=b,m、n属于自然数且n>m,求Sn? 设数列an的前n项和为Sn,满足an+sn=An^2+Bn+1(A不等于0)an为等差数列,求(B-1)/A 已知等差数列(an)的前n项和为Sn,且a3=5,S15=225,设bn=2^a n+2n,求数已知等差数列(an)的前n项和为Sn,且a3=5,S15=225,设bn=2^a n+2n,求数列{bn}的前n项和Tn 已知数列{an}的前n项和Sn,且a1=a(a为非零常数),当n>=2时,an=2Sn^2/2已知数列{an}的前n项和Sn,且a1=a(a为非零常数),当n>=2时,an=2Sn^2/2Sn-11)求证:数列{1/Sn}是等差数列2)设bn=Sn/an,数列bn的前n项和为Tn.已 设等差数列{an}的前n项和为Sn,且a4-a2=8,S10=190,(1)求等差数列{an}的通项公式an 设等差数列{an}的前n项和为Sn ,且S15>0,a8+a90,a8+a9 设等差数列{An}的前n项和为Sn,且A5=5A3,则S9/S5=? 设等差数列{an}的前n项和为Sn,已知a3=12,且S12>0,S13