数列{an}中,an+1+an=2n-44(n属于N+),a1=-23 (1)求an.(2)设Sn为{an}的前n项和,求Sn1)求an.(2)设Sn为{an}的前n项和,求Sn (n+1是a角标)
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![数列{an}中,an+1+an=2n-44(n属于N+),a1=-23 (1)求an.(2)设Sn为{an}的前n项和,求Sn1)求an.(2)设Sn为{an}的前n项和,求Sn (n+1是a角标)](/uploads/image/z/2131960-40-0.jpg?t=%E6%95%B0%E5%88%97%7Ban%7D%E4%B8%AD%2Can%2B1%2Ban%3D2n%EF%BC%8D44%28n%E5%B1%9E%E4%BA%8EN%2B%29%2Ca1%3D-23+%EF%BC%881%EF%BC%89%E6%B1%82an.%EF%BC%882%EF%BC%89%E8%AE%BESn%E4%B8%BA%7Ban%7D%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8C%2C%E6%B1%82Sn1%EF%BC%89%E6%B1%82an.%EF%BC%882%EF%BC%89%E8%AE%BESn%E4%B8%BA%7Ban%7D%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8C%2C%E6%B1%82Sn+%EF%BC%88n%2B1%E6%98%AFa%E8%A7%92%E6%A0%87%29)
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数列{an}中,an+1+an=2n-44(n属于N+),a1=-23 (1)求an.(2)设Sn为{an}的前n项和,求Sn1)求an.(2)设Sn为{an}的前n项和,求Sn (n+1是a角标)
数列{an}中,an+1+an=2n-44(n属于N+),a1=-23 (1)求an.(2)设Sn为{an}的前n项和,求Sn
1)求an.(2)设Sn为{an}的前n项和,求Sn (n+1是a角标)
数列{an}中,an+1+an=2n-44(n属于N+),a1=-23 (1)求an.(2)设Sn为{an}的前n项和,求Sn1)求an.(2)设Sn为{an}的前n项和,求Sn (n+1是a角标)
a(n+1)+an=2n-44
a(n+2)+a(n+1)=2(n+1)-44
两式相减得
a(n+2)-an=2
又a2+a1=2-44,
a2=-19,a1=-23
偶数项成等差数列 奇数项成等差数列
a1=-23 a2=-19
a(2n-1)=2n-25,a2n=2n-21
于是an=n-24 (n为奇数) an=n-21(n为偶数)
2)当n为奇数时
sn=(a1+a3+.+an)+(a2+a4+.+an-1)
=[-23+(-21)+.+n-24]+[-19+(-17)+.+n-23]
=(2n^2-89n-5)/4