设数列{an}满足关系an=3/2(an-1)+5(n≥2),a1=-17/2.令bn=an+10,求数列{bn}的前n项和Sn

来源:学生作业帮助网 编辑:六六作业网 时间:2024/11/28 08:20:43
设数列{an}满足关系an=3/2(an-1)+5(n≥2),a1=-17/2.令bn=an+10,求数列{bn}的前n项和Sn设数列{an}满足关系an=3/2(an-1)+5(n≥2),a1=-1

设数列{an}满足关系an=3/2(an-1)+5(n≥2),a1=-17/2.令bn=an+10,求数列{bn}的前n项和Sn
设数列{an}满足关系an=3/2(an-1)+5(n≥2),a1=-17/2.令bn=an+10,求数列{bn}的前n项和Sn

设数列{an}满足关系an=3/2(an-1)+5(n≥2),a1=-17/2.令bn=an+10,求数列{bn}的前n项和Sn
an-3/2(an-1) =5 (1)式
(an-1) - 3/2(an-2) =5 (2)式 .
(an-2) - 3/2(an-3) =5 (3)式 .
.
.
a2- 3/2(a1) =5 (n-1)式
上述(2)式乘以3/2,上述(3)式乘以(3/2)^2,.上述(n-1)式乘以(3/2)^n-2,将全部n-1个等式相加,就得到:
an - a1(3/2)^n-1 = 5+ 5x(3/2) + 5x(3/2)^2 + .+ 5x(3/2)^n-2(本步骤中x代表乘号)
等式右侧是个首项5,公比3/2的等比数列的n-1项求和,所以它等于10(3/2)n-1 - 10
即:an - a1(3/2)^n-1 = 10(3/2)n-1 - 10
将 a1= -17/2带入,得到an = (3/2)^n -10
所以bn = (3/2)^n; bn是个首项3/2,公比3/2的等比数列
Sn = 3(3/2)^n -3

若数列{An},满足关系a1=2,an+1=3an+2,求数列的通项公式 设数列{an}满足an=2an-1+n 若{an}是等差数列,求{an}通项公式 数列{an}满足a1=3/2,an+1=an2-an+1,求证:1/an=1/(an)-1 - 1/(an+1)-1数列{an}满足a1=3/2,an+1=an2-an+1,求证:1/an=1/(an)-1 - 1/(an+1)-1设Sn=1/a1+1/a2+...+1/an,n>2证明1 数列AN满足A1=2,AN+1=AN^2+6AN+6,设CN=LOG5(AN+3),证{CN}为等比 数列{an}满足a1=1,且an=an-1+3n-2,求an 设数列{an}满足关系an=3/2(an-1)+5(n≥2),a1=-17/2.令bn=an+10,求数列{bn}的前n项和Sn 设数列{an}满足关系an=3/2(an-1)+5(n≥2),a1=-17/2.令bn=an+10,求数列{bn}的前n项和Sn 设数列AN满足A1等于1,3(A1+a2+~+AN)=(n+2)an,求通向公式 数列 (10 18:35:56)设数列{an}满足a1=9,an+1=-1/2an+3,求an的通项公式(含过程) 设数列{an}满足:a1+a2/2+a3/3+a4/4……+an/n=An+B,其中A、B为常数.数列{an}是否为等差数列? 关于数列、等差数列的题目设数列an满足an+1=an-2且a1=241)判断an是什么数列2)若an 已知数列{an}满足:a1=3,an+1=(3an-2)/an ,n∈N*.(Ⅰ)证明数列{(an-1)/an-2已知数列{an}满足:a1=3,an+1=(3an-2)/an ,n∈N*.(1)证明数列{(an-1)/an-2 }为等比数列,并求数列{an}的通项公式;(2)设设b 设数列{an}满足a1=1, an=(4an-1 +2)/(2an-1 +7) ,则通项xn=? 已知数列an满足 a1=1/2,an+1=3an/an+3求证1/an为等差数列已知数列an满足 a1=1/2,an+1=3an/an+3求证1/an为等差数列 设数列an满足a1=2,a(n+1)=3an+2^(n-1),求an2,设数列an满足a1=2,a(n+1)=3an+2n,求an 设数列,a1=3,an+1=3an-2,求数列an是等比数列 设数列{an}满足a1=1a2=2an=1/3(an-1+2an-2)求an题目为设数列{an}满足a1=1,a2=2,an=1/3(an-1+2an-2)求an 已知数列{an}满足a1=1,a2=3,an+2=3an+1-2an求an