在数列{an}中,a1=2,an+1=an+2n,则an=_.

问题描述:

在数列{an}中,a1=2,an+1=an+2n,则an=______.

∵在数列{an}中,a1=2,an+1=an+2n,∴a2-a1=2,a3-a2=4,a4-a3=6,…an+1-an=2n,∴an=a1+(a2-a1)+(a3-a2)+…+(an-an-1)=2+2+4+6+…+2(n-1)=2+2×(1+2+3+…+n-1)=2+n(n-1)=n2-n+2.∴an=n2−n+2.故答...