已知等比数列{an}前n项和为Sn,且满足S3=72,S6=632,(Ⅰ)求数列{an}的通项公式;(Ⅱ)求log2a1+log2a

2025-06-29 02:51:34
推荐回答(1个)
回答1:

(Ⅰ)由题意可得,公比q≠1,再由S3=

7
2
,S6=
63
2
可得
a1(1-q3)
1-q
=
7
2
a1(1-q6)
1-q
=
63
2

解得
a1=
1
2
q=2
,故通项公式为 an=
1
2
?2n-1=2n-2
(Ⅱ)由(Ⅰ)可得log2an=n-2,
∴log2a1+log2a2+log2a3+…+log2a25
=-1+0+1+2+…+23
=
25(-1+23)
2

=275.