内蒙古赤峰市曾有一道中考题如下:观察一组式子:3~2+4~2=5~2,5~2+12~2=13~2,7~2+24~2=25~2,9~2+40~2=41~2,…猜想一下第n个式子是.一、解法探究观察所给的四个式子___,它们都满足a~2+b~2=c~2,我们知道满足a~2+b~2=c~2的正整数a、b、c叫勾股数.其中,第一个数为奇数,最大的数与较大的数差为1. Chifeng City, Inner Mongolia had a middle school exam questions are as follows: observe a set of formulas: 3 ~ 2 +4 ~ 2 = 5 ~ 2,5 ~ 2 +12 ~ 2 = 13 ~ 2,7 ~ 2 +24 ~ 2 = 25 ~ 2,9 ~ 2 + 40 ~ 2 = 41 ~ 2, ... guess the nth formula is. First, the solution to explore the observation of the four formulas ___, they all satisfy a ~ 2 + b ~ 2 = c ~ 2, we know that the positive integers a, b, c that satisfy a ~ 2 + b ~ 2 = c ~ 2 are called the number of shares, of which the first number is odd number, the difference between the largest number and the larger number is 1.