Question

已知等差数列{an}的公差和等比数列{bn}的公比是同一个非零实数d,且a1=b1,a4=b4,

Answer 1

an=a1+(n-1)d

bn=b1*d^(n-1)

因a1=b1,a4=b4

a1+3d=a1*d^3,a1=3d/(d^3-1)

又a10=b10,a1=9d/(d^9-1)

∴1/(d^3-1)=3/(d^9-1)

因d≠1,所以d=-2^(1/3)

a1=2^(1/3),b16=an,

n=32