已知等差数列的前n项和为Sn,若S13=-26,a9=4,求:(1)数列的通项公式;(2)a1+a3+a5+…+a2n-1

2025-06-20 09:33:42
推荐回答(1个)
回答1:

(1)由题意可得S13=

13(a1+a13)
2
=
13×2a7
2
=13a7=-26,
解之可得a7=-2,故公差d=
a9-a7
9-7
=3 …(6分)
故可得an=a9+(n-9)d=3n-23…(7分)
(2)由(1)可知a2n-1=3(2n-1)-23=6n-26,
且数列a1,a3,a5,…a2n-1.仍成等差数列
a1+a3+…+a2n-1=
n(a1+a2n-1)
2

=
n(-20+6n-26)
2
=3n2-23n
…(13分)