已知数列an满足a1=1,a3+a7=18

来源：学生作业帮编辑：拍题作业网作业帮分类：数学作业时间：2024/04/27 21:36:09

a1=1,a3+a7=18,
a(n+1)+a(n-1)=2an
a(n+1)-an = an - a(n-1)
a(n+1)-an= a7-a6 (1)
a(n+1)-an= a6-a5 (2)
a(n+1)-an= a5-a4 (3)
a(n+1)-an= a4-a3 (4)
a(n+1)-an= a3-a2 (5)
a(n+1)-an= a2-a1 (6)
(1)+(2)+(3)+(4)+2(5)+2(6)
8[a(n+1)-an]= a7+a3- 2a1
=18 -2
a(n+1)-an=2
an -a1=2(n-1)
an = 2n-1
(2)
let
S= 1.2^1+2.2^2+...+n.2^n (1)
2S= 1.2^2+2.2^3...+n.2^(n+1) (2)
(2)-(1)
S= n.2^(n+1) -(2+2^2+...+2^n)
=n.2^(n+1) -2(2^n -1)
cn=2^(n-1).an
= 2^(n-1).( 2n-1)
= n.2^n - 2^(n-1)
Tn=c1+c2+...+cn
=S - (2^n-1)
= n.2^(n+1) -3(2^n -1)
= 3+ (2n-3).2^n

已知数列an满足a1=1,a3+a7=18 已知数列an满足a1=1,a3+a7=18,且(an-1)+(an+1)=2an(n>=2) 已知数列{an}满足a1=1，a3+a7=18，且an-1+an+1=2an（n≥2）．急用!数列{an}满足a1=1,a3+a7=18. 已知等差数列{an}公差为d,满足a1+a2+a3=15,且a1+1,a3+1,a7+1构成等你数列的连续三项已知数列{an}满足a1=1,a3+a7=18,且an-1+an+1=2an(n大于等于2) (1)求数列(an)的通项已知数列{An}满足A1=1,A3+A7=18,且A（n-1）+A（n+1）=2An若Cn=2^n-1*An,求{Cn} 已知数列{an}满足a1+a2+a3+...+an=n^2+2n.(1)求a1,a2,a3,a4 已知等差数列{an}中,a1=1,a7=4,数列{bn}是等比数列,b1=6,b2=a3. 已知等差数列{an}是递增数列,且满足a4.a7=15,a3+a8=8 已知数列{an}满足a1+a2+a3+.+an=n的平方,求数列通项已知数列{an}满足a1=1;an=a1+2a2+3a3+...+(n-1)a(n-1);