设数列{an}的前n项和为Sn,Sn=a1(3n−1)2(对于所有n≥1),且a4=54,则a1的数值是_.

问题描述:

设数列{an}的前n项和为Sn,Sn=

a1(3n−1)
2
(对于所有n≥1),且a4=54,则a1的数值是______.

设数列{an}的前n项和为Sn,Sn=

a1(3n−1)
2
(对于所有n≥1),
则a4=S4-S3=
a1(81−1)
2
a1(27−1)
2
=27a1

且a4=54,则a1=2
故答案为2