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=
(对于所有n≥1),且a4=54,则a1的数值是______.
a1(3n−1) 2
答
设数列{an}的前n项和为Sn,Sn=
(对于所有n≥1),
a1(3n−1) 2
则a4=S4-S3=
−
a1(81−1) 2
=27a1,
a1(27−1) 2
且a4=54,则a1=2
故答案为2