数列{an}满足an+1+an=4n-3(n∈N*).若{an}满足a1=2,Sn为{an}的前n项和,求S2n+1.详细一点

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数列{an}满足an+1+an=4n-3(n∈N*).若{an}满足a1=2,Sn为{an}的前n项和,求S2n+1.详细一点
数列{an}满足an+1+an=4n-3(n∈N*).若{an}满足a1=2,Sn为{an}的前n项和,求S2n+1.
详细一点

数列{an}满足an+1+an=4n-3(n∈N*).若{an}满足a1=2,Sn为{an}的前n项和,求S2n+1.详细一点
a(n+1)+a(n)=4n-3
a(n+2)+a(n+1)=4n+1
a(n+2)-a(n)=4
a(1)=2,a(3)=6,a(5)=10,a(2n+1)=4n+2
a(2)+a(1)=1,a(2)=-1,a(4)=3,a(2n)=4n-5
S(2n+1)=a(1)+...+a(2n+1)+a(2)+...a(2n)=(2n+2)*(n+1)+(2n-3)*n=4n^2+n+2