设正项数列{an}前n项和是sn,若{an},{根号下sn}都是等差数列,且等差相等,则a1等于?

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：2024/09/23 04:33:40

{an},{√sn}都是等差数列,
∴2√S2=√S1+√S3,
即2√（2a1+d)=√a1+√（3a1+3d),
平方得4(2a1+d)=a1+3a1+3d+2√[a1(3a1+3d)],
4a1+d=2√[a1(3a1+3d)],
平方得16a1^2+8a1d+d^2=4a1(3a1+3d),
4a1^2-4a1d+d^2=0,
d=2a1.
又两数列公差相等,
∴√（4a1)-√a1=2a1,a1>0,
∴1=2√a1,a1=1/4.

设正项数列{an}前n项和是sn,若{an},{根号下sn}都是等差数列,且等差相等,则a1等于? 设正项数列an的前n项和是Sn并且对于任意n∈N+ a1与1的等差中项等于根号下Sn 求数列已知数列an是等差数列,且a1不等于0,Sn为这个数列的前n项和,求limnan/Sn.limSn+Sn-1/Sn+Sn 求极限,数列An是等差数列,且A1不等于0,Sn是前N项和一道数列题目数列{an}的前n项和为Sn,且an是Sn和1的等差中项,等差数列{bn}满足b1=a1,b4=a4 求数列已知数列{an}的前n项和为Sn,且满足an+2Sn*Sn-1=0,a1=1/2.求证：{1/Sn}是等差数列已知数列{an}的前n项和为Sn,且满足Sn=Sn-1/2Sn-1 +1,a1=2,求证{1/Sn}是等差数列已知数列an是等差数列,且a1≠0,Sn为这个数列的前n项和.求1、lim nan/Sn 2、lim (Sn+Sn+1) 高三数列难题已知正项等差数列An>0,且前n项和为Sn,满足{An}和{根号Sn}都是等差数列,且公差相等,求An的通项已知数列an的前n项和为Sn,且an是Sn和1的等差中项,等差数列bn满足b1=a1,b4=S3, 若等差数列{an}的首项为a1,公差为d,前n项的和为Sn,则数列(Sn/n)为等差数列,且通项已知数列{an}的前n项和为Sn,首项为a1,且1,an,Sn等差数列