Question

已知在等比数列{an},公比q>1,且a1+a4=9,a2*a3=8,则(a2011+a2012)/(a2009+a20

Answer 1

解:a1＋a4=a1＋a1q^3=9(1),a2*a3=a1q^3=8(2)

由(1)(2)解得a1=1,q=2,

所以(a2012＋a2013)/(a2010＋a2011)

=(a2010q^2＋a2010q^3)/(a2010＋a2010q)

＝(q^2＋q^3)/(1＋q)

=q^2=2^2

=4