等差数列{an}的前n项和为Sn,且6S5-5S3=5,则a4=_.

问题描述:

等差数列{an}的前n项和为Sn,且6S5-5S3=5,则a4=______.

∵Sn=na1+

1
2
n(n-1)d
∴S5=5a1+10d,S3=3a1+3d
∴6S5-5S3=30a1+60d-(15a1+15d)
=15a1+45d=15(a1+3d)=15a4=5
解得a4=
1
3

故答案为:
1
3