等比数列{an},an>0,q≠1,且a2,(1/2)a3,a1成等差数列,则(a3+a4)/(a4+a5)=
问题描述:
等比数列{an},an>0,q≠1,且a2,(1/2)a3,a1成等差数列,则(a3+a4)/(a4+a5)=
答
设{an}的公比为q.a1=a2/q,a3=a2*q∵a2,(1/2)*a3,a1成等差数列∴2*(1/2)*a3=a2+a1 a2*q=a2+a2/qa2为等比数列中的项 ∴a2≠0 左右同乘q/a2,q²-q-1=0q=(1-根5)/2或q=(1+根5)/2因为an>0,所以q>0,q=(1+根5)/2(a...