等差数列{an}共有2n+1项,其中奇数项之和为4,偶数项之和为3,则n的值是(  ) A.3 B.5 C.7 D.9

问题描述:

等差数列{an}共有2n+1项,其中奇数项之和为4,偶数项之和为3,则n的值是(  )
A. 3
B. 5
C. 7
D. 9

设数列公差为d,首项为a1
奇数项共n+1项,其和为S=

(n+1)(a1+a2n+1)
2
=
(n+1)2an+1
2
=(n+1)an+1=4,①
偶数项共n项,其和为S=
n(a2+a2n)
2
=
n2an+1
2
=nan+1=3,②
得,
n+1
n
4
3
,解得n=3
故选A