等差数列{an}中 前n项和为Sn a3=7 S4=24

1.求通项公式an2.求和a1+a3+a5+...+a2n+13.求数列{Sn/n}前n项和Pn
2025-05-14 13:07:23
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回答1:

① an=2n+1
a3=a1+2d S4=4a1+6d=24 4a3=4a1+8d S4-4a3= -2d = -4 ∴d=2
a1=3 → an=2n+1

② 设 bn=4n-1 Tn=b1+b2+b3+……+bn
a1+a3+a5+...+a2n+1
=T(n+1)= 2n^2 + 5n +3

③ 易知 Sn=n^2 +2n
则Sn/n= n+2 Pn=1/2 ( n^2 + 5n)