解析:选A ==
==×=1.
6.若等差数列{an}的前n项和为Sn=An2+Bn,则该数列的公差为________.
解析:数列{an}的前n项和为Sn=An2+Bn,所以当n≥2时,an=Sn-Sn-1=An2+Bn-A(n-1)2-B(n-1)=2An+B-A,当n=1时满足,所以d=2A.
答案:2A
7.设等差数列{an}的前n项和为Sn,且Sm=-2,Sm+1=0,Sm+2=3,则m=________.
解析:因为Sn是等差数列{an}的前n项和,所以数列是等差数列,所以+=,即+=0,解得m=4.
答案:4
8.设项数为奇数的等差数列,奇数项之和为44,偶数项之和为33,则这个数列的中间项是________,项数是________.
解析:设等差数列{an}的项数为2n+1,
S奇=a1+a3+...+a2n+1
=
=(n+1)an+1,
S偶=a2+a4+a6+...+a2n==nan+1,
所以==,解得n=3,所以项数2n+1=7,
S奇-S偶=an+1,即a4=44-33=11为所求中间项.
答案:11 7
9.已知数列{an}的前n项和为Sn,且满足log2(Sn+1)=n+1,求数列{an}的通项公式.
解:由已知条件,可得Sn+1=2n+1,
则Sn=2n+1-1.
当n=1时,a1=S1=3,
当n≥2时,an=Sn-Sn-1=(2n+1-1)-(2n-1)=2n,
又当n=1时,3≠21,
故an=