{an}是公差不为0的等差数列,若a7,a10,a11是等比数列{bn}中的连续三项,又b1=1,则bn=?
问题描述:
{an}是公差不为0的等差数列,若a7,a10,a11是等比数列{bn}中的连续三项,又b1=1,则bn=?
答
a7=a1+6da10=a1+9da11=a1+10d(a10)^2=a7*a11a1^2+18a1*d+81d^2=a1^2+16a1*d+60d^2所以a1=-21d/2.a10=-3d/2,a11=-d/2.因此{bn}的公比q=a11/a10=1/3b1=1所以bn=b1*q^(n-1)=1/3^(n-1).