已知等差数列｛an｝的前n项和为Sn＝n2＋pn＋q（p,q∈R）,且a2,a3,a5成等比数列

来源：学生作业帮编辑：大师作文网作业帮分类：数学作业时间：2024/11/12 08:27:55

已知等差数列｛an｝的前n项和为Sn＝n2＋pn＋q（p,q∈R）,且a2,a3,a5成等比数列
求p,q的值

若数列｛bn｝满足an＋log2n＝log2bn,求数列｛bn｝的前n项和Tn

(1)
Sn = n^2+pn+q
n=1 ,a1= p+q+1
an = Sn - S(n-1)
= 2n-1 + p (1)
a1= 1+p = p+q+1
=>q=0
from (1)
a2 = 3+p
a3 =5+p
a5 = 9+p
a2,a3 ,a5成等比数列
a2.a5 = (a3)^2
(3+p)(9+p)=(5+p)^2
12p+27 = 10p+25
p=-1
(2)
an = 2n-2
an+logn=logbn
2n-2 = log(bn/n)
bn/n = 2^(2n-2)
bn = n.2^(2n-2)
let
S = 1.2^0 + 2.2^2 + .+n.2^(2n-2) (2)
4S = 1.2^2 + 2.2^4 + .+n.2^(2n) (3)
(3)-(2)
3S = n.2^(2n) - [ 1 + 2^2+2^4+...+2^(2n-2) ]
= n.2^(2n) - (1/3)(2^(2n) -1)
S = 3n.2^(2n) - (2^(2n) -1)
= 1 + (3n-1).2^(2n)
Tn = b1+b2+...+bn=S =1 + (3n-1).2^(2n)

数列题.已知等差数列an的前n项为Sn=n²+pn+q(p,q∈R)，且a2,a3,a5成等比数列1.求p,, 已知等差数列{an}的前n项的和为Sn=pn^2-2n+q（p,q属于R）,求q的值已知数列{an}是首项a1=4,公比q不等于1的等比数列,Sn是其前n项和,且4a1,a5,-2a3成等差数列已知等比数列{an}中，公比q∈R，且a1+a2+a3=9，a4+a5+a6=-3，Sn为数列{an}的前n项和，则li 已知{an}是首项为1,公比为q的等比数列,且a4,a6,a5成等差数列,求an的前n项和Sn 已知数列an是首项为4公比为q的等比数列,sn是其前n项和,且4a1,a5,-2a3成等差数列,求设An=S1+S2+… 已知等比数列{an}的公比为q,前n项和为Sn,且S3,S9,S6成等差数列,给出下列结论：①a3,a9,a6成等差数列等比数列{an}的前n项和为Sn,已知S1,S3,S2成等差数列,求{an}的公比Q.已知a1-a3=3,求sn? 已知等比数列{An}的公比为q,前n项的和为Sn,且S3,S9,S6成等差数列. 已知等比数列{An}的公比为q,前n项和为Sn,且S3,S9,S6成等差数列已知Sn是等比数列｛an}的前n项和,a2.a8,a5成等差数列求解一道数列的题已知等差数列{an}的前n项和Sn=pn²-2n+q (p,q∈R）.n∈N+(1)求q的值要