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=
,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).
2n−1(n为正奇数) 2n−1(n为正偶数)
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
=
+2×1−45
1−4
(2+8)-44 2
=
+40-4
45−1 3
=341+36
=377.
故答案为:256,377.