作业帮设公差d不等于0的等差数列{an}和等比数列{bn}满足a1=b1,a3=b3,a7=b5,求使an=bm成立的n与m的
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设公差d不等于0的等差数列{an}和等比数列{bn}满足a1=b1,a3=b3,a7=b5,求使an=bm成立的n与m的函数关系式n=f（m）
A1=B1 A3=B3 A7=B5
A3=A1+2d=B3=B1×q^2
A7=A1+6d=B5=B1×q^4
A1+2d=A1×q^2 3A1+6d=3A1×q^2
A1+6d=A1×q^4
2A1=3A1×q^2-A1×q^4
q^4-3q^2+2=0
q^2=1 q^2=2
q^2=1时,d=0（舍去）
q^2=2 A1+2d=2A1 d=A1/2
An=A1+(n-1)d=A1+(n-1)A1/2=A1(n+1)/2
Bm=B1×q^(m-1)=A1×2^[(m-1)/2]
An=Bm
A1(n+1)/2=A1×2^[(m-1)/2]
(n+1)/2=2^[(m-1)/2]
n+1=2×2^[(m-1)/2]=2^[(m+1)/2]
n=2^[(m+1)/2]-1
A3=A1+2d=B3=B1×q^2
A7=A1+6d=B5=B1×q^4
A1+2d=A1×q^2 3A1+6d=3A1×q^2
A1+6d=A1×q^4
2A1=3A1×q^2-A1×q^4
q^4-3q^2+2=0
q^2=1 q^2=2
q^2=1时,d=0（舍去）
q^2=2 A1+2d=2A1 d=A1/2
An=A1+(n-1)d=A1+(n-1)A1/2=A1(n+1)/2
Bm=B1×q^(m-1)=A1×2^[(m-1)/2]
An=Bm
A1(n+1)/2=A1×2^[(m-1)/2]
(n+1)/2=2^[(m-1)/2]
n+1=2×2^[(m-1)/2]=2^[(m+1)/2]
n=2^[(m+1)/2]-1
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