下列数列是等差数列的是( )
A、an=n2 |
B、Sn=2n+1 |
C、Sn=2n2+1 |
D、Sn=2n2-n |
考点:等差关系的确定
专题:等差数列与等比数列
分析:利用等差数列的概念,对A、B、C、D四个选项逐一判断即可.
解答: 解:A:∵an=n2,∴a1=1,a2=4,a3=9,显然4-1≠9-4,故数列{an}不是等差数列;
B:∵Sn=2n+1,∴Sn+1=2(n+1)+1=2n+3,Sn+1-Sn=2,故数列{Sn}是等差数列;
C:∵Sn=2n2+1,∴Sn+1=2(n+1)2+1=2n2+4n+3,Sn+1-Sn=4n+2,不是定值,故数列{Sn}不是等差数列;
D:∵Sn=2n2-n,∴Sn+1=2(n+1)2-(n+1)=2n2+3n+1,Sn+1-Sn=4n+1,不是定值,故数列{Sn}不是等差数列;
故选:B.
B:∵Sn=2n+1,∴Sn+1=2(n+1)+1=2n+3,Sn+1-Sn=2,故数列{Sn}是等差数列;
C:∵Sn=2n2+1,∴Sn+1=2(n+1)2+1=2n2+4n+3,Sn+1-Sn=4n+2,不是定值,故数列{Sn}不是等差数列;
D:∵Sn=2n2-n,∴Sn+1=2(n+1)2-(n+1)=2n2+3n+1,Sn+1-Sn=4n+1,不是定值,故数列{Sn}不是等差数列;
故选:B.
点评:本题考查等差关系的确定,深刻理解等差数列的概念是关键,想当然地认为Sn是数列{an}的前n项和是易错点,属于中档题.