若数列{an}满足a1=1,a(n+1)=an+2n,且n属于正整数,则a100=

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若数列{an}满足a1=1,a(n+1)=an+2n,且n属于正整数,则a100=若数列{an}满足a1=1,a(n+1)=an+2n,且n属于正整数,则a100=若数列{an}满足a1=1,a(n+

若数列{an}满足a1=1,a(n+1)=an+2n,且n属于正整数,则a100=
若数列{an}满足a1=1,a(n+1)=an+2n,且n属于正整数,则a100=

若数列{an}满足a1=1,a(n+1)=an+2n,且n属于正整数,则a100=
a100=9901
a(n+1)-an=2n
a(n)-a(n-1)=2(n-1)
a(n-1)-a(n-2)=2(n-2)
………………
a2-a3=4
a2-a1=2
累加,得:a(n)-a1=2n*½(n-1)=n²-n
∴an=n²-n+1
∴a100=9901
参考一下

a2=a1+2*1
a3=a2+2*2=a1+2*1+2*2
a4=a3+2*4=a1+2*1+2*2+2*3
a100=1+2*1+2*2+2*3+.....+2*99=1+2*(1+99)*99/2=9901

9901

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