已知数列{an}的前n项和Sn=-2n2+5n(n∈N*).(1)求数列{an}的通项公式;(2)如果两个互不相等的正整数

2025-06-22 20:18:50
推荐回答(1个)
回答1:

(1)当n=1时,a1=3,--------------1’
当n≥2时,an=Sn-Sn-1=-2n2+5n-[-2(n-1)2+5(n-1)]=-4n+7---------------3’
当n=1时满足通项公式,∴an=-4n+7---------4’
(2)∵n1n2

n1+n2
2
=q,
Sn1+Sn2
2
?Sq
1
2
(?2
n
+5n1?2
n
+5n2)?(?2q2+5q)
----6’
=
1
2
[?2(
n
+
n
)+10q]+2q2?5q
=?(
n
+
n
)+2(
n1+n2
2
)2
=?
1
2
[2
n
+2
n
?(n1+n2)2]
=
1
2
(n1?n2)2<0
-------10’
Sn1+Sn2
2
Sq
-----------12’