已知两个等比数列{an},{bn}的前n项和分别为Sn,Tn,且满足SnTn=2n−13n−1,则a7b7=_.

问题描述:

已知两个等比数列{an},{bn}的前n项和分别为Sn,Tn,且满足

Sn
Tn
=
2n−1
3n−1
,则
a7
b7
=______.

设两个等比数列的公比分别为q,q′,则

Sn
Tn
=
2n−1
3n−1

qn−1
qn−1
=
2n−1
3n−1

∴q=2,q′=3,
a7
b7
=
1
2
×
q6
q6
=
32
729

故答案为:
32
729