数列{an}中,a1=1,an+1=an+2n,则an=()A.n2-n+1B.n2+1C.(n-1)2+1D.2n-数学

题目简介

数列{an}中,a1=1,an+1=an+2n,则an=()A.n2-n+1B.n2+1C.(n-1)2+1D.2n-数学

题目详情

数列{an}中,a1=1,an+1=an+2n,则an=(  )
A.n2-n+1B.n2+1C.(n-1)2+1D.2n
题型:单选题难度:中档来源:不详

答案

数列{an}中,a1=1,an+1=an+2n,
∴an+1-an=2n,
a2-a1=2,
a3-a2=4,

an+1-an=2n,
进行叠加可得,an+1-a1=2+4+6+…+2n=
n(2+2n)
2
=n(n+1),
∴an+1=1+n(n+1),
∴an=n(n-1)+1=n2-n+1,
故选A;

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