已知数列{an}是等差数列,且a1=2,a1+a2+a3=12.(1)求数列{an}的通项公式;(2)令bn=an2an,求数列{b

2025-05-12 19:11:50
推荐回答(1个)
回答(1):

(1)由已知a1=2,a1+a2+a3=12,得a1+a1+d+a1+2d=12,即a1+d=4,
则a2=4,又a1=2,
∴d=2,an=2+2(n-1)=2n;
(2)由(1)知bn

2n
4n
,设数列{bn}前n项和为Sn,则Sn=
2
4
+
2×2
42
+…+
2n
4n
①,
Sn
4
=
2
16
+
2×2
43
+
2×3
44
+…+
2(n?1)
4n
+
2n
4n+1
②,
又①-②错位相减得:
3
4
Sn=
1
2
+
1
4
-
1
8
+
2
43
(1+
1
4
+…+
2
4n?3
)-
2n
4n+1

=
5
8
+
1
32
×
1?
1
4n?2
1?
1
4
-