数列{an}是公差为1的等差数列.数列{bn}满足b1=1,bn=3an+2
(1)求证{bn}是等差数列 (2)求{bn}的通项公式
人气:288 ℃ 时间:2019-10-24 13:57:00
解答
1)bn=3an+2
∴b﹤n-1﹥=3a﹤n-1﹥+2
bn-b﹤n-1﹥=3an+2-(3a﹤n-1﹥+2)=3(an-a﹤n-1﹥)=3*1=3
∴{bn}是以b1=1为首项,d=3为公差的等差数列
2)bn=b1+(n-1)d=1+(n-1)*3=3n-2
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