已知等差数列{an}的公差和等比数列{bn}的公比都是d,又知d≠1,且a4=b4,a10=b10已知等差数列{an}的公差和等比数列{bn}的公比都是d,又知d≠1,且a1=b1,a4=b4,a10=b10:(1)求a1与d的值; (2)b16是不是{an}中的项
问题描述：
已知等差数列{an}的公差和等比数列{bn}的公比都是d,又知d≠1,且a4=b4,a10=b10
已知等差数列{an}的公差和等比数列{bn}的公比都是d,又知d≠1,且a1=b1,a4=b4,a10=b10:(1)求a1与d的值; (2)b16是不是{an}中的项
答
a4=a1+3db4=b1*d^3所以a1+3d=a1*d^3 a1=3d/(d^3-1)a10=a1+9db10=b1*d^9所以a1+9d=a1*d^9a1=9d/(d^9-1)所以3d/(d^3-1)=9d/(d^9-1)d^9-1=3d^3-3d^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)=0d不等于1,...