Question

设S_n为等比数列{a_n}的前n项和，a₆=8a₃，则

S6

S3

=______．

Answer 1

∵S_n为等比数列{a_n}的前n项和，
a₆=8a₃，
∴

a6

a3

=

a1q5

a1q2

=q3=8，
∴q=2，
∴

S6

S3

=

a1(1-26) 1-2

a1(1-23) 1-2

=

1-26

1-23

=

1-64

1-8

=

63

7

=9．
故答案为：9．