设Sn是等差数列{an}的前n项和,若a7a4=2,则S13S7的值为_.

问题描述:

设Sn是等差数列{an}的前n项和,若

a7
a4
=2,则
S13
S7
的值为______.

由题意可得

S13
S7
=
13(a1+a13)
2
7(a1+a7)
2
=
13(a1+a13)
7(a1+a7)

=
13×2a7
7×2a4
=
13
7
×
a7
a4
=
13
7
×2
=
26
7

故答案为:
26
7