设数列{an}、{bn}各项都是正数,a1=1,b1=2,若lgbn,lgan+1,lgbn+1成等差数列,5an,5b
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/10/04 14:07:58
设数列{an}、{bn}各项都是正数,a1=1,b1=2,若lgbn,lgan+1,lgbn+1成等差数列,5an,5bn,5an+1成等比数
列,求an,bn通项公式
列,求an,bn通项公式
lgbn,lgan+1,lgbn+1成等差数列,5an,5bn,5an+1成等比数就得到
①(an+1)^2=bn*bn+1
②bn^2=an*an+1
①*①
(an+1)^4=bn^2*(bn+1)^2=an*(an+1)^2*(an+2)
(an+1)^2=an*an+2
所以an是个等比数列.
由②可得
b1^2=a1*a2
那么a2=4
∴an=4^(n-1)
bn^2=4^(n-1)*4^n=4^(2n-1)
bn=(4^n)/2
①(an+1)^2=bn*bn+1
②bn^2=an*an+1
①*①
(an+1)^4=bn^2*(bn+1)^2=an*(an+1)^2*(an+2)
(an+1)^2=an*an+2
所以an是个等比数列.
由②可得
b1^2=a1*a2
那么a2=4
∴an=4^(n-1)
bn^2=4^(n-1)*4^n=4^(2n-1)
bn=(4^n)/2
设数列{an}、{bn}各项都是正数,a1=1,b1=2,若lgbn,lgan+1,lgbn+1成等差数列,5an,5b
设各项均为正数的数列{an}和{bn}满足5^an,5^bn,5^an+1成等比数列,lgbn,lgan+1,lgbn+
有两个各项都是正数的数列an,bn,如果a1=1,b1=2,a2=3且an,bn,an+1成等差数列
有两个各项an,bn都是正数的数列和,如果a1=1,b1=2,a2=3,且an,bn,an+1成等差数列,bn,an+1
设各项均为正数的数列{an}和{bn}满足:an,bn,an+1成等差数列,bn,an+1,bn+1等比数列且a1=1,
数列an,bn各项均为正数,a1=1,b1=2,a2=3,对任意n,an,bn,an+1成等差数列,bn,an+1,bn
已知数列{an},{bn}都是公差为1的等差数列,其首项分别为a1,b1,且a1+b1=5,a1,b1∈N*,设c
设数列{An}的各项都是正数,且A1=1,(An)+1/(An+1)+1=(An+1)/2An,Bn=An平方+An.
设数列{an}的各项都是正数,a1=1,(an+1)/(an+1+1)=an+1/2an,bn=an2+an.(1)求数
设数列{an}是等差数列,{bn}为各项都为正数的等比数列.且a1=b1=1,a3+b5=21,a5+b3=13.
数列{an}、{bn}分别为正项等比数列,Tn,Rn分别是数列{lgan}{lgbn}的前n项和,且Tn/Rn=n/2n
设数列{An}{Bn} 满足A1=B1= A2=B2=6 A3=B3=5且{An+1-An}是等差数列{Bn+1-Bn}