问题详情:
设a1=22-02,a2=32-12,…,an=(n+1)2-(n-1)2(n为大于1的整数)
(1)计算a15的值;
(2)通过拼图你发现前三个图形的面积之和与第四个正方形的面积之间有什么关系:
__________________________________(用含a、b的式子表示);
① ② ③ ④
(3)根据(2)中结论,探究an=(n+1)2-(n-1)2是否为4的倍数.
【回答】
(1)a15=162-142=256-196=60·······································································(2分)
(2) (a+b)2=a2+2ab+b2 ··············································································(4分)
(3) an=(n+1)2-(n-1)2 =(n2+2n+1)-(n2-2n+1) =n2+2n+1-n2+2n-1=4n
w W w .X k b 1.c O m
是4的倍数. ···············································································(6分)
知识点:有理数的乘方
题型:解答题