数列an是等差数列,bn是等比数列,满足b1=a1^2,b2=a2^2,b3=a3^2,求数列bn公比q

数列an是等差数列,bn是等比数列,满足b1=a1^2,b2=a2^2,b3=a3^2,求数列bn公比q

设an公差是d,
因为b1*b3=(b2)^2
所以a1^2*(a1+2d)^2=[(a1+d)^2]^2
(a1^2+2a1d)^2[(a1+d)^2]^2=0
[a1^2+2a1d+(a1+d)^2][a1^2+2a1d-(a1+d)^2]=0
所以a1^2+2a1d+(a1+d)^2=0,
或a1^2+2a1d-(a1+d)^2=0
若a1^2+2a1d-(a1+d)^2=0,则d=0,不合
若a1^2+2a1d+(a1+d)^2=0,
即2a1^2+4a1d+d^2=0
亦即2(a1/d)^2+4a1/d+1=0
解得a1/d=-1±√2/2
若a1/d=-1-√2/2
公比q=b2/b1=(a2/a1)^2=(1+d/a1)^2=(√2-1)^2=3-2√2
若a1/d=-1+√2/2
公比q=b2/b1=(a2/a1)^2=(1+d/a1)^2=（-1-√2）^2=3+2√2

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