数学“数列”问题

来源：百度知道 编辑：UC知道 时间：2024/07/02 05:28:26
如果一个数列{cn}的各项既是等差数列中的项,又是等比数列的项,我们就称之为“和谐数列”，现已知等差数列{an}的公差和等比数列{bn}的公比都是d（不等于1），且a1=b1 a4=b4 a10=b10
分别求出数列{an} {bn}
一定要快啊！！！！！！！！1

a4=a1+3d
b4=b1*d^3
所以a1+3d=a1*d^3
a1=3d/(d^3-1)

a10=a1+9d
b10=b1*d^9
所以a1+9d=a1*d^9
a1=9d/(d^9-1)
所以3d/(d^3-1)=9d/(d^9-1)
d^9-1=3d^3-3
d^9-3d^3+2=0
(d^9-1)-3(d^3-1)=0
(d^3-1)(d^6+d^3+1)-3(d^3-1)=0
d不等于1，所以d^3-1不等于0
所以(d^6+d^3+1)-3=0
d^6+d^3-2=0
(d^3+2)(d^3-1)=0
d^3-1不等于0
d^3=-2
d=-2^(1/3)
a1=3d/(d^3-1)=2^(1/3)=b1
则an=2^(1/3)+(n-1)*[-2^(1/3)]
=-2^(1/3)n+2^(4/3)
bn=2^(1/3)*[-2^(1/3)]^(n-1)

zzzzz

a1=b1
a4=a1+3d=b4=b1*d³
a10=a1+9d=b4=b1*d^9
整理得
3d/(d^3-1)=9d/(d^9-1)
d^9-1=3d^3-3
d^9-3d^3+2=0
(d^9-1)-3(d^3-1)=0
(d^3-1)(d^6+d^3+1)-3(d^3-1)=0
d≠1，所以d^3-1≠0
所以(d^6+d^3+1)-3=0
d^6+d^3-2=0
(d^3+2)(d^3-1)=0
d^3-1不等于0
d^3=-2
d=-2^(1/3)
a1=3d/(d^3-1)=2^(1/3)=b1
则an=2^(1/3)+(n-1)*[-2^(1/3)]
=-2^(1/3)n+2^(4/3)
bn=2^(1/3)*[-2^(1/3