已知数列{an}中,an=2n−1(n为正奇数)2n−1(n为正偶数),则a9=_(用数字作答),设数列{an}的前n项和为Sn,则S9=_(用数字作答).

问题描述:

已知数列{an}中,an=

2n−1(n为正奇数)
2n−1(n为正偶数)
,则a9=______(用数字作答),设数列{an}的前n项和为Sn,则S9=______(用数字作答).

∵数列{an}中,an=

2n−1(n为正奇数)
2n−1(n为正偶数)

∴a9=29-1=28=256.
S9=21-1+(2×2-1)+23-1+(2×4-1)+25-1+(2×6-1)+27-1+(2×8-1)+29-1
=(20+22+24+26+28)+2(2+4+6+8)-1×4
=
1−45
1−4
+2×
4
2
(2+8)
-4
=
45−1
3
+40-4
=341+36
=377.
故答案为:256,377.