已知等差数列{an}的首项a1=1,且对于n∈N*,S2n/Sn为常数,求数列{an}的通项公式

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：2024/11/20 15:13:21

设公差 = d
an = a1 + (n-1) d = 1+ (n-1)d
Sn = (1 + 1+(n-1)d) * n /2 = (2+(n-1)d) n/2
a2n = a1 + (2n-1)d = 1 +(2n-1)d
S2n = (1 + 1+(2n-1)d) * (2n)/2 =(2+(2n-1)d) *(2n) /2
S2n/ Sn = (2+(2n-1)d)*2 / (2+(n-1)d)
S2/S1 = (2+(2-1)d) / a1 = 2+d
所以 n>1 时
(2+(2n-1)d)*2 / (2+(n-1)d) = 2+d
(2+(2n-1)d)*2 = (2+d) (2+(n-1)d)
整理得
(n-1)*d^2 -2nd +2d =0
(n-1)d(d-2) =0
所以
d = 0 或 d=2
{an}的通项公式为
an = a1 + (n-1) *0 = 1
或
an = a1 + (n-1) *2 = 1 + 2n -2 = 2n -1

已知数列前n项和为Sn,首项为a1,且1,an,Sn为等差数列 (1)求数列{an}的通项公式已知数列an的前n项和为Sn,首项伟a1,且1,an,Sn成等差数列,求数列an的通项公式设数列an的前n项和为Sn,其中an不等于0,a1=a(常数),且a1,an,Sn成等差数列 (1)求an的通项公式已知数列{an}a1=2前n项和为Sn 且满足Sn Sn-1=3an 求数列{an}的通项公式an 已知数列{an}为等差数列,Sn为其前n项和,且a1=10,s12=-125求数列{an}的通项公式an 已知数列{log2^(an+1)}(n∈N)为等差数列,且a1=1,a3=7.求(1)求数列{an}的通项公式(2)数列已知数列an的前n项和为Sn,且an+2Sn*Sn-1=0,a1=1/2,求证1/SN是等差数列,求数列SN的的通项公式数列：已知数列{an}前 n项和为Sn,且a1=2,4Sn=ana(n+1).求数列{an}的通项公式. 已知数列an的前n项和为Sn,且a1=1,an=2Sn^2/2Sn -1（n≥2,n∈N+）求数列an的通项公式已知数列{an}的前N项和为Sn 且an+1=Sn-n+3,a1=2,.求an的通项公式设数列{an}的前n项和为Sn,其中an不等于0,a为常数,且-a1,sn,an+1成等差数列,求{an}的通项公式已知数列An中,其前n项和为Sn,A1=1,且An+1=2Sn 求数列an的通项公式