问题 填空题
研究下列算式:
1×3+1
=
4
=2;
2×4+1
=
9
=3;
3×5+1
=
16
=4;
4×6+1
=
25
=5;…请你找出规律,并用正整数n表示为:______.
答案

第一个式子:

1×(1+2)+1
=
(1+1)2
=1+1;

第二个式子:

2×(2+2)+1
=
(2+1)2
=2+1;

第三个式子:

3×(3+2)+1
=
(3+1)2
=3+1;

第四个式子:

4×(4+2)+1
=
(4+1)2
=4+1;

故第n个式子为:

n(n+2)+1
=
(n+1)2
=n+1.

故答案为:

n(n+2)+1
=
(n+1)2
=n+1.

推断题
单项选择题