已知{an}为等比数列,{bn}为等差数列,其中a2=b4,a3=b2,a4=b1,且a1=64,公式q≠1,求an,bn.
问题描述：
已知{an}为等比数列,{bn}为等差数列,其中a2=b4,a3=b2,a4=b1,且a1=64,公式q≠1,求an,bn.
答
设公差为d,公比为q,则a2=b4a3=b2a4=b1a2-a3=b4-b2=2da3-a4=b2-b1=da1q-a1q^2=2da1q^2-a1q^3=da1q-a1q^2=2a1q^2-2a1q^31-q=2q-2q^22q^2-3q+1=0(2q-1)(q-1)=0q=1/2或q=1（不合题意,舍去）an=64/2^(n-1)=2^6/2^(n-1)=2^...