已知数列{an}满足a(n+1)=an+3n+2,且a1=2,求an=?
人气:464 ℃ 时间:2020-02-18 17:06:26
解答
a(n+1)-an=3n+2
所以
an-a(n-1)=3(n-1)-2
a(n-1)-a(n-2)=3(n-2)-2
……
a2-a1=3*1-2
相加
an-a1=3[1+2+……+(n-1)]-2(n-1)
=3n(n-1)/2-2(n-1)
=(3n²-7n+4)/2
a1=2
an=(3n²-7n+8)/2
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