已知数列{an}中a1=1,点(an,an+1)在函数y=3x+2的图象上(n∈N*). (I)证明:数列{an+1}是等比数列; (Ⅱ)求数列{an}的前n项和.
问题描述:
已知数列{an}中a1=1,点(an,an+1)在函数y=3x+2的图象上(n∈N*).
(I)证明:数列{an+1}是等比数列;
(Ⅱ)求数列{an}的前n项和.
答
证明:(I)由题意可得,an+1=3an+2则an+1+1=3(an+1)且a1+1=2∴数列{an+1}是以2为首项,以3为公比的等比数列(II)由(I)可得,an+1=2•3n−1∴an=2•3n−1−1∴Sn=(2•30−1)+(2•3−1)+…+(2•3n−1−1)=2(...