(1)正确.在等差数列{
an}中,
Sn=
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123520318500.gif)
,则
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123520333425.gif)
(
a1+
an),这表明点(
an,
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123520146360.gif)
)的
坐标适合方程
y![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123520364235.gif)
(
x+
a1),于是点(
an,
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123520146360.gif)
)均在直线
y=
x+
a1上
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/2014082312352019381.gif)
(2)正确
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/2014082312352019381.gif)
设(
x,
y)∈
A∩
B,则(
x,
y)中的坐标
x,
y应是方程组
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123520474789.gif)
的解,由方程组消去
y得:2
a1x+
a12=-4(
*),当
a1=0时,方程(
*)无解,此时
A∩
B=
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123520302206.gif)
;当
a1≠0时,方程(
*)只有一个解
x=
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123520505447.gif)
,此时,方程组也只有一解
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123520520818.gif)
,故上述方程组至多有一解
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/2014082312352019381.gif)
∴
A∩
B至多有一个元素
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/2014082312352019381.gif)
(3)不正确.取
a1=1,
d=1,对一切的
x∈N
*,有
an=
a1+(
n-1)
d=
n>0,
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123520146360.gif)
>0,这时集合A中的元素作为点的坐标,其横、纵坐标均为正,另外,由于
a1=1≠0
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/2014082312352019381.gif)
如果
A∩
B≠
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123520302206.gif)
,那么据(2)的结论,
A∩
B中至多有一个元素(
x0,
y0),而
x0=
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123520645522.gif)
<0,
y0=
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123520661473.gif)
<0,这样的(
x0,
y0)
A,产生矛盾,故
a1=1,
d=1时
A∩
B=
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123520302206.gif)
,所以
a1≠0时,一定有
A∩
B≠
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823123520302206.gif)
是不正确的.